## Publications

- Shimura sums related to quadratic imaginary fields

*Proceedings of the Japan Academy of Sciences***70**(A), No. 5, 1994, pp. 146-151 - Congruences on the Fourier coefficients of modular forms on Γ
_{0}(N)

The Rademacher Legacy to Mathematics,*Contemporary Mathematics***166**, 1994, pp. 93-105 - On the positivity of the number of partitions that are t-cores

*Acta Arithmetica***66**, No. 3, 1994, pp. 221-228 - Superlacunary cusp forms
*(with Sinai Robbins)*

*Proceedings of the America Mathematical Society***123**, No. 4, 1995, pp. 1021-1029 - Parity of the partition function

*Electronic Research Announcements of the American Mathematical Society***1**, No. 1, 1995, pp. 35-42 - On the representation of integers as sums of triangular number
*(with Sinai Robbins and Patrick Wahl)*

*Aequationes Mathematica***50**, 1995, pp. 73-94 - A note on the number of t-core partitions

*The Rocky Mountain Journal of Mathematics***25**, No. 3, 1995, pp. 1165-1169 - A note on the Shimura correspondence and the Ramanujuan τ(n) function

*Utilitas Mathematica***47**, 1995, pp. 170-180 - Congruences for Frobenius partitions

*Journal of Number Theory***57**, No. 1, 1996, pp. 331-347 - Defect zero p-blocks for finite simple groups
*(with Andrew Granville)*

*Transactions of the American Mathematical Society***348**, No. 1, 1996, pp. 331-347 - On the parity of the partition function in arithmetic progressions

*Journal fur die reine und angewandte Mathematik***472**, 1996, pp. 1-15 - Congruences for the Fourier coefficients of half-integral weight modular forms and special values of L-functions
*(with Antal Balog and Henri Darmon)*

*Proceedings for a Conference in Honor of Heini Halbestam***1**, 1996, pp, 105-128 - Congruences for partition functions
*(with Dennis Eichlorn)*

*Proceedings for a Conference in Honor of Heini Halbertstam***1**, 1996, pp, 309-321 - Rank zero quadratic twists of modular elliptic curves

*Compositio Mathematica***104**, 1996, 293-304 - Quadratic forms and elliptic curves III
*(with Takashi Ono)*

*Proceedings of the Japan Academy of Sciences***72**(A), 1996, pp. 204-205 - Euler's concordant forms

*Acta Arithmetica***65**, 1996, pp. 101-123 - Some recurrences for arithmetical functions
*(with Neville Robbins and Brad Wilson)*

*Journal of the Indian Mathematical Society***62**, 1996, pp, 29-50 - Divisibility properties of certain partition functions by powers of primes
*(with Basil Gordon)*

*The Ramanujan Journal***1**, 1997, pp, 25-35 - Parity of the Fourier coefficients of modular forms
*(with Brad Wilson)*

*Illinois Journal of Mathematics***41**, 1997, pp. 142-150 - Odd values of the partition function

*Discrete Mathematics***169**, 1997, pp. 263-268 - 4-core partitions and class numbers
*(with Lawrence Sze)*

*Acta Arithmetica***65**, 1997, pp. 249-272 - Twists of elliptic curves

*Compositio Mathematica***106**, 1997, pp. 349-360 - Ramanujan, taxicabs, birthdates, zipcodes and twists

*American Mathematical Monthly***104**, No. 10, 1997, pp. 912-917 - Tate-Shafarevich groups of the congruent number elliptic curves

*Acta Arithmetica***81**, 1997, pp. 247-252 - Ramanujan's ternary quadratic form
*(with Soundararajan Kannan)*

*Inventiones Mathematicae***130**, No. 3, 1997, pp. 415-454 - Eta-quotients and elliptic curves
*(with Yves Martin)*

*Proceedings of the American Mathematical Society***125**, 1997, pp. 3169-3176 - Values of Gaussian hypergeometric series

*Transactions of the American Mathematical Society***350**, No. 3, 1998, pp. 1205-1223 - A binomial coefficient identity related to a conjecture of F. Beukers
*(with Scott Ahlgren, Shalosh Ekhad, Doron Zeilberger)*

*Electronic Journal of Combinatorics***5**, No. 1, 1998, R10 - Fourier coefficients of half-integral weight modular forms modulo l
*(with Chris Skinner)*

*Annals of Mathematics***147**, No. 2, 1998, pp. 453-470 - Gordon's ε-conjecture on the lacunarity of modular forms

*Comptes Rendues Math. Rep. of Acad. Sci. Canada***20**, No. 4, 1998, pp, 103-107 - Partitions into distinct parts and elliptic curves

*Journal of Combinatorial Theory***82**(A), 1998, pp. 193-201 - A note on a question of J. Nekovar and the Birch and Swinnerton-Dyer Conjecture

*Proceedings of the American Mathematical Society***126**, 1998, pp. 2849-2853 - The residue of p(n) modulo small primes

Erdos Memorial Issue,*The Ramanujan Journal***2**, 1998, pp, 47-54 - The partition function in arithmetic progressions

*Mathematische Annalen***312**, 1998, pp, 251-260 - Rook theory and t-cores
*(with Jim Haglund and Lawrence Sze)*

*Journal of Combinatorial Theory***84**(A), 1998, pp. 9-37 - Corrigendum: Fourier coefficients of half-integral weight modular forms modulo l
*(wtih Chris Skinner)*

*Annals of Mathematics***148**, 1998, p. 361

*A typesetting error occured in #29* - Nonvanishing of quadratic twists of modular L-functions
*(with Chris Skinner)*

*Inventiones Mathematicae***134**, 1998, pp. 651-660 - Integers represented by ternary quadratic forms
*(with Soundararajan Kannan)*

Proceedings of the 5^{th}Meeting of the Canadian Number Theory Association,*CRM Proceedings and Lecture Notes***19**, 1998, pp. 527-532 - A note on the irreducibility of Hecke polynomials
*(with Kevin James)*

*Journal of Number Theory***73**, 1998, pp. 527-532 - Nonvanishing of values of modular L-functions and some applications
*(with Jan Hendrick Bruinier, Kevin James, Winfried Kohnene, Vinayak Vatsal, Chris Skinner)*

*Proceedings of Topics in Number Theory*, Kluwer Academic Publishers, 1999, pp. 115-126 - Theorems and conjectures involving rook polynomials with real roots
*(with Jim Haglund and David Wagner)*

*Proceedings of Topics in Number Theory*, Kluwer Academic Publishers, 1999, pp. 207-222 - Indivisibility of class numbers of imaginary quadratic fields and orders of Tate-Shafarevich groups of elliptic curves with complex multiplication
*(with Winfried Kohnen)*

*Inventiones Mathematicae***135**, 1999, pp. 387-398 - Selmer groups of quadratic twists of modular elliptic curves
*(with Kevin James)*

*Mathematische Annalen***314**, 1999, pp. 1-17 - Ramanujan's unpublished manuscript on the partition and tau functions with commentary
*(with Bruce Berndt)*

*The Andrews Festchrift*, (eds.) D. Foata, G.-N. Han, Springer Verlag, 2001, pp. 39-110 - On the circular summation of the eleventh powers of Ramanujan's theta function

*Journal of Number Theory***76**, 1999, pp. 62-65 - Indivisibility of class numbers of real quadratic fields

*Compositio Mathematica***119**, 1999, pp. 1-11 - The partition function and the arithmetic of certain modular L-functions
*(with Li Guo)*

*International Mathematical Research Notices*, 1999, No. 21, pp. 1179-1197 - Distribution of the partition function modulo m

*Annals of Mathematics***151**, 2000, pp. 293-307 - A Gaussian hypergeometric series evaluation and Apery number congruences
*(with Scott Ahlgren)*

*Journal fur die reine und angewandte Mathematik***518**, 2000, pp. 187-212 - Modularity of a certain Calabi-Yau threefold
*(with Scott Ahlgren)*

*Monatshefte fur Mathematik***129**, 2000, pp. 177-190 - On "good" half-integral weight modular forms
*(with Jorge Jimenez-Urroz)*

*Mathematics Research Letters***7**, No. 2, 2000, pp. 205-212 - The 2-adic behavior of the number of partitions into distinct parts
*(with David Penniston)*

*Journal of Combinatorial Theory***92**(A), 2000, pp. 138-157 - Nonvanishing of quadratic twists of modular L-functions with applications for elliptic curves

*Journal fur die reine und angewandte Mathematik***533**, 2001, pp. 81-97 - Differential endomorphisms for modular forms on Γ
_{0}(4)

*Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics*, (eds.) F. Garvan, M. Ismail, Kluwer Academic Publishers, 1999, pp. 223-230 - q-series identities and values of certain L-functions
*(with George Andrews and Jorge Jimenez-Urroz)*

*Duke Mathematical Journal***108**, 2001, pp. 395-419 - Corrigendum: The 2-adic behavior of the number of partitions into distinct parts
*(with David Penniston)*

*Journal of Combinatorial Theory***95**(A), 2001, p. 196

*Theorem 11 of #52 was stated incorrectly* - Parity of the partiton function in arithmetic progressions II
*(with Matthew Boylan)*

*Bulletin of the London Mathematical Society***33**, No. 5, 2001, pp. 558-564 - Addition and counting: The arithmetic of partitions
*(with Scott Ahlgren)*

*Notices of the American Mathematical Society***48**, October 2001, pp. 978-984 - Arithmetic of the partition function

*Proceedings of the NATO Advances Study Institute on Special Functions, Special Functions 2000*, (eds.) J. Bustoz, S. Suslov, Kluwer Academic Publishers, pp. 243-253 - Prime power degree representations of the symmetric and alternating groups
*(with Antal Balog, Christine Bessenrodt, Jorn Olsson)*

*Journal of the London Mathematical Society***64**, 2001, pp. 344-356 - Congruence properties for the partition function
*(with Scott Ahlgren)*

*Proceedings of the National Academy of Sciences*, USA,**98**, Issue 23, 2001, pp. 12882-12884 - The Chebotarev density theorem in short intervals and some questions of Serre
*(with Antal Balog)*

*Journal of Number Theory***91**, 2001, pp. 356-371 - Congruences and conjectures for the partition function
*(with Scott Ahlgren)*

Proceedings of the Conference on q-series with Applications to Combinatorics, Number Theory and Physics,*AMS Contemporary Mathematics***291**, 2001, pp 1-10 - Extension of Ramanujan's congruences for the partition function modulo powers of 5
*(with Jeremy Lovejoy)*

*Journal fur die reine angewandte Mathematik***542**, 2002, pp. 123-132 - Zeta functions of an infinite family of K3 surfaces
*(with Scott Ahlgren and David Penniston)*

*American Journal of Mathematics***124**, 2002, pp. 353-368 - Representations of integers as sums of squares

*Journal of Number Theory***95**, 2002, pp. 253-258 - A q-series identity and the arthmetic of Hurwitz zeta-functions
*(with Gwynneth Coogan)*

*Proceedings of the American Mathematical Society***131**, 2003, pp. 719-724 - Quadratic twists of modular forms and elliptic curves
*(with Matthew Papanikolas)*

*Proceedings of the Millenial Number Theory Conference*, (eds.) M.A. Bennet, et. al., Vol. III, A.K. Peters, 2002, pp. 73-86 - Congruences for
_{3}F_{2}hypergeometric functions over finite fields*(with David Penniston)*

*Illinois Journal of Mathematics***46**, 2002, pp. 679-684 - Weierstrass points on X
_{0}(p) and supersingular j-invariants*(with Scott Ahlgren)*

*Mathematiche Annalen***325**, 2003, pp. 355-368 - Coefficients of half-integral weight modular forms
*(with Jan Bruinier)*

*Journal of Number Theory***99**, 2003, pp. 164-179 - Modular form congruences and Selmer groups
*(with William McGraw)*

*Journal of the London Mathematical Society***67**, 2003, pp. 302-318 - Arithmetic of the coefficients of Cohen's Eisenstein series
*(with Antal Balog and William McGraw)*

*Acta Arithmetica***107**, 2003, pp. 337-344 - Hypergeometric generating functions for the values of Dirichlet and other L-functions
*(with Jeremy Lovejoy)*

*Proceedings of the National Academy of Sciences*, USA,**100**, No. 12, 2003, pp. 6904-6909 - Baxter algebras and Hopf algebras
*(with George Andrews, Li Guo, William Keigher)*

*Transactions of the American Mathematical Society***355**, 2003, pp. 4639-4656 - The life and work of R.A. Rankin
*(with Bruce Berndt and Winfried Kohnen)*

*The Ramanujan Journal***7**, 2003, pp. 11-40 - Elements of class groups and Shafarevich-Tate groups of elliptic curves
*(with Antal Balog)*

*Duke Mathematical Journal***120**, 2003, pp. 35-63 - Arithmetic of Borcherds' exponents
*(with Jan Bruinier)*

*Mathematische Annalen***327**, 2003, pp. 293-303 - p-adic properties of the values of the j-function
*(with Matt Papanikolas)*

*Galois Theory and Modular Forms*, (eds.) K. Hashimoto, K. Miyake, H. Nakamura, Kluwer Academic Publishers, 2003, pp. 357-366 - The arithmetic of the values of modular functions and the divisors of modular forms
*(with Jan Bruinier and Winfried Kohnen)*

*Compositio Mathematica***140**, 2004, pp. 552-566. - Arithmetic of certain hypergeometric modular forms
*(with Karl Mahlburg)*

*Acta Arithmetica***113**, 2004, pp. 39-55. - Hecke operators and the q-expansion of modular forms

*Proceedings of the 7*, Montreal 2002, CRM Conference Proceedings and Lecture Notes^{th}Meeting of the Canadian Number Theory Association**36**, 2004, American Mathematical Society, pp. 229-235. - Arithmetic of singular moduli and class polynomials
*(with Scott Ahlgren)*

*Compositio Mathematica*,**141**, 2005, pp. 293-312. - Gaussian hypergeometric functions and Hecke operators
*(with Sharon Frechette and Matt Papanikolas)*

*International Mathematical Research Notices*,**60**, 2004, pp. 3233-3262. - Corrigendum: Coefficients of half-integral weight modular forms
*(with Jan Bruinier)*

*Journal of Number Theory***104**, 2004, pp. 378-379.

*The hypothesis that M is prime is needed from Theorems 1 and 2.3 of #71* - 2-adic properties of certain modular forms and their applications to arithmetic functions
*(with Yuichiro Taguchi)*,

*International Journal of Number Theory*,**1**, No. 1 2005, pp. 75-101. - Partitions and McKay numbers for Sn ,

*Journal of Combinatorial Theory, Series A*,**108**, 2004, pages 185-197. - The combinatorics of traces of Hecke operators
*(with Sharon Frechette and Matt Papanikolas)*

*Proceedings of the National Academy of Sciences, USA,***101**No. 49, 2004, pages 17016-17020. - Linear relations between modular form coefficients and non-ordinary primes
*(with YoungJu Choie and Winfried Kohnen)*,

*Bulletin of the London Mathematical Society,***37**, Part 3, 2005, pages 335-341. - Hilbert class polynomials and traces of singular moduli
*(with Jan Bruinier and Paul Jenkins)*,

*Mathematische Annalen,***334**no. 2, 2006, pages 373-393. - On the work of Basil Gordon
*(with George E. Andrews, Krishnaswami Alladi, and Richard McIntosh)**,*

Note added in the proof,

*Journal of Combinatorial Theory, Series A,***113**, 2006, pages 21-38. - Reduction of CM elliptic curves and modular function congruences
*(with Noam D. Elkies and Tonghai Yang)*,

*International Mathematical Research Notices,***44**(2005), pages 2695-2707. - Identities for traces of singular moduli
*(with Kathrin Bringmann)*,

*Acta Arithmetica,***119**(2005), pages 317-327. - Number theoretic properties of Wronskians of Andrews-Gordon series
*(with Antun Milas and Eric Mortenson)*,

*International Journal of Number Theory,***4**(2008), pages 323-337. - Traces of singular moduli on Hilbert modular surfaces
*(with Kathrin Bringmann and Jeremy Rouse)*,

*International Mathematical Research Notices,***47**(2005), pages 2891-2912. - Arithmetic properties of coefficients of half-integral weight Maass-Poincare series
*(with Kathrin Bringmann)*,

*Mathematische Annalen,***337**(2007), pages 591-612. - An arithmetic formula for the partition function
*(with Kathrin Bringmann)*,

*Proceedings of the American Mathematical Society,***135**(2007), pages 3507-3514. - The $f(q)$ mock theta function conjecture and partition ranks
*(with Kathrin Bringmann)*,

*Inventiones Mathematicae,***165**(2006), pages 243-266. - Singular moduli generating functions for modular curves and surfaces, The Proceedings of the Gauss-Dirichlet Conference, Clay Mathematical Institute Proceedings, Clay Math. Proc.
**7**, Amer. Math. Soc. (2007), pages 185-206. - Dyson's ranks and Maass forms,
*(with Kathrin Bringmann)*,

*Annals of Mathematics,***171**(2010), pages 419-449. - Ramanujan's congruences and Dyson's crank
*(with George Andrews)*,

*Proceedings of the National Academy of Sciences, USA,***102**, No. 43 (2005), page 15277. - Mock theta functions, ranks, and Maass forms, Surveys in Number Theory, Developments in Mathematics (Ed. K. Alladi)
**17**, Springer-Verlag, 2008, pages 119-142. - Honoring a gift from Kumbakonam,

*Notices of the American Mathematical Society,***53**, Number 6 (2006), pages 640-651. - Divisibility criteria for class numbers of imaginary quadratic fields,
*(with Paul Jenkins)*,

*Acta Arithmetica,***125**(2006), pages 285-289. - q-series and weight 3/2 Maass forms
*(with Kathrin Bringmann and Amanda Folsom)*,

*Compositio Mathematica,***145**(2009), pages 541-552. - Lifting elliptic cusp forms to Maass forms with an application to partitions
*(with Kathrin Bringmann)*,

*Proceedings of the National Academy of Sciences, USA,***104**, No. 10 (2007), pages 3725-3731. - Duality involving the mock theta function f(q)
*(with Amanda Folsom)*,

*Journal of the London Mathematical Society,***77**(2008), pages 320-334. - Eulerian series as modular forms
*(with Kathrin Bringmann and Rob Rhoades)*,

*Journal of the American Mathematical Society,***21**(2008), pages 1085-1104. - Heegner divisors, L-functions, and Maass forms
*(with Jan H. Bruinier)*,

*Annals of Mathematics,***172**(2010), pp. 2135-2181. - Algebraicity of harmonic Maass forms,

SASTRA Prize volume,*Ramanujan Journal,***20**(2009), pages 297-309. - The
*spt*-function of Andrews*(with Amanda Folsom)*,

*Proceedings of the National Academy of Sciences, USA,***105**no. 51 (2008), pages 20152-20156.*Theorem 1.2 is not correctly stated. One must replace pm^2 by p^(4a+1)m^2 where gcd(p,m)=1.* - A mock theta function for the Delta-function,

*Proceedings of the 2007 Integers Conference,*Combinatorial Number Theory: Proceedings of the 2007 Integers Conference, de Gruyter, Berlin, 2009, pages 141-156. - Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues,
*(with Jan H. Bruinier and Robert Rhoades)*,

(formerly*Differential operators and harmonic weak Maass forms*)

*Mathematische Annalen,***342**(2008), pages 673-693. - Unearthing the visions of a master: harmonic Maass forms and number theory,

*Proceedings of the 2008 Harvard-MIT Current Developments in Mathematics Conference,*International Press, Somerville, MA, 2009, pages 347-454. - Coefficients of harmonic weak Maass forms,
*(with Kathrin Bringmann)*, Partitions,*q*-series and modular forms, Dev. 23, Springer Verlag, New York, 2012, 23-38.

*Proceedings of the 2008 University of Florida Conference on Partitions, q-series, and modular forms.* - Modular forms arising from
*Q(n)*and Dyson's rank*(with Maria Monks)*, Dennis Stanton special issue of*Advances in Applied Mathematics*,**46**(2011), pages 457-466. - Hook lengths and 3-cores,
*(with Guo-Niu Han)*,

*Annals of Combinatorics*,**15**(2011), pages 305-312. *SO(3)*-Donaldson invariants of*CP^2*and mock theta functions,*(with Andreas Malmendier)*,*Geometry and Topology,***16**(2012), pages 1767-1833.- Corrigendum: Duality involving the mock theta function
*f(q)**(with Amanda Folsom)*

*Journal of the London Mathematical Society,***79**(2009), page 544.

*Some numbers in Table 1.3 of #107 are corrected.* - Lehmer's conjecture on Ramanujan's tau-function,

*Journal of the Indian Mathematical Society*, (2008), Special Centenary Issue, pages 149-163. - Probabilities as values of modular forms and continued fractions
*(with Riad Masri)*,

*International Journal of Mathematics and the Mathematical Sciences,*(2009), Article ID 941920. - Some characters of Kac and Wakimoto and nonholomorphic modular functions
*(with Kathrin Bringmann)*,

*Mathematische Annalen*,**345**(2009), pages 547-558. - Identities and congruences for the coefficients of Ramanujan's
*omega(q)**(with Jan H. Bruinier)*,*Ramanujan Journal***23**(2010), pages 151-157. - Corrigendum: Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues
*(with Jan H. Bruinier and Rob Rhoades)*

*Mathematische Annalen,***345**(2009), page 31.

*The statement of Theorem 1.4 and a related sentence in #113 are corrected.* -
*p*-adic coupling of mock modular forms and shadows,*(with Pavel Guerzhoy and Zach Kent)*,

*Proceedings of the National Academy of Sciences, USA,***107**no. 14 (2010), pages 6169-6174. - The parity of the partition function,

*Advances in Mathematics,***225**(2010), pages 349-366. - The last words of a genius,

*Notices of the American Mathematical Society*,**57**(2010), pages 1410-1419. - Gauss's 2F1 hypergeometric function and the congruent number elliptic curve,
*(with Ahmad El-Guindy)*,

*Acta Arithmetica,***144**(2010), pages 231-239. -
Hasse invariants for the Clausen elliptic curves,
*(with Ahmad El-Guindy)*,*Ramanujan Journal*,**31**(2013), pages 3-13. - Eichler-Shimura theory for mock modular forms,
*(with Kathrin Bringmann, Pavel Guerzhoy, and Zach Kent)*,*Mathematische Annalen*,**355**(2013), pages 1085-1121. - Congruences for the Andrews
*spt-*function,*Proceedings of the National Academy of Sciences, USA*,**108**(2011), pages 473-476. - The partition function and Hecke operators,
*Advances in Mathematics*,**228**(2011), pages 527-534. *l*-adic properties of the partition function*(with Amanda Folsom and Zach Kent)*,*Advances in Mathematics*,**229**(2012), pages 1586-1609.- Algebraic formulas for the coefficients of half-integral weight harmonic weak
Maass forms
*(with Jan Bruinier)*,*Advances in Mathematics*,**246**(2013), pages 198-219. - A mod
*l*Atkin-Lehner theorem and applications*(with Nick Ramsey)*,*Archiv der Mathematik,***98**(2012), pages 25-36 (Birkhauser-Verlag*Distinguished Article*). -
Class polynomials for nonholomorphic modular functions,
*(with Jan Bruinier and Andrew V. Sutherland)*, Winnie Li Special Issue of*Journal of Number Theory*,**161**(2016), pages 204-229. - SU(2) Donaldson invariants of the projective plane,
*(with Michael Griffin and Andreas Malmendier)*,*Forum Mathematicum*,**27**(2015), pages 2003-2023. - ``Tribute to Basil Gordon''
*(with Krishnaswami Alladi, George Andrews, Robert Guralnick, Bruce Rothschild),**Notices of the American Mathematical Society*,**60**, No. 7, 2013, pages 856-865. - Srinivasa Ramanujan - going strong at 125, Part II,
*(with George Andrews, Bruce Berndt, Manjul Bhargava, Jon Borwein, Kannan Soundararajan, Robert Vaughan, Ole Warnaar),**Notices of the American Mathematical Society*,**60**(2013), pages 10-22. - Unimodal sequences and quantum and mock modular forms,
*(with Jennifer Bryson, Sarah Pitman, and Robert C. Rhoades),**Proceedings of the National Academy of Sciences, USA,***109**, No. 40 (2012), pages 16063-16067. - Moonshine for M24 and Donaldson invariants for CP^2,
*(with Andreas Malmendier)**Communications in Number Theory and Physics,***6**(2012), pages 759-770. - Mock theta functions and quantum modular forms,
*(with Amanda Folsom and Rob Rhoades)**Forum of Mathematics, Pi,***1**(2013), e2, 27 pages. - Recent work on the partition function,
*(with Jan H. Bruinier, Amanda Folsom, and Zach Kent)**Proceedings of the Legacy of Ramanujan Conference,*New Delhi, Ramanujan Math. Soc. Lect. Notes, No. 20, 2013, pages 139-151. - Ramanujan's radial limits,
*(with Amanda Folsom and Rob Rhoades)*,*Proceedings of the Ramanujan 125 Conference at the University of Florida,*Contemp. Math.**627**2014, Amer. Math. Soc., pages 91-102. - Ramanujan's mock theta functions,
*(with Michael Griffin and Larry Rolen),**Proceedings of the National Academy of Sciences, USA*,**110**, No. 15 (2013), pages 5765-5768. - Weierstrass mock modular forms and elliptic curves,
*(with Claudia Alfes, Michael Griffin and Larry Rolen),**Research in Number Theory,***1: 24**(2015). - Classical and umbral Moonshine: connections and $p$-adic properties,
*(with Sarah Trebat-Leder and Larry Rolen),**Journal of the Ramanujan Mathematical Society*,**30**, No. 2 (2015), pages 135-159.. - A framework of Rogers-Ramanujan identities and their arithmetic properties,
*(with Michael Griffin and S. Ole Warnaar),**Duke Mathematical Journal,***165**(2016), pages 1475-1527. - Maximal multiplicative properties of partitions
*(with Christine Bessenrodt),**Annals of Combinatorics*,**20**(2016), pages 59-64. - Special values of shifted convolution Dirichlet series
*(with Michael Mertens),**Mathematika*,**62**(2016), pages 47-66. - Moonshine
*(with John F. R. Duncan and Michael Griffin),**Research in the Mathematical Sciences,***2**(2015), A11. *p*-adic properties of modular shifted convolution Dirichlet series*(with Kathrin Bringmann and Michael Mertens),**Proceedings of the American Mathematical Society,***144**(2016), pages 1439-1452.- Proof of the Umbral Moonshine Conjecture
*(with John F. R. Duncan and Michael Griffin),**Research in the Mathematical Sciences,***2: 26**(2015). -
The Jack Daniels Problem
*(with John F. R. Duncan),*Winnie Li Special Issue of*Journal of Number Theory*,**161**(2016), pages 230-239. -
The 1729
*K3*surface*(with Sarah Trebat Leder),**Research in Number Theory,***2**(2016), 2: 26. - A note on nonordinary primes
*(with Seokho Jin and Wenjun Ma),**Proceedings of the American Mathematical Society,***144**(2016), pages 4591-4597. - The Riemann Hypothesis for period polynomials of modular forms
*(with Seokho Jin, Wenjun Ma, and Kannan Soundararajan),**Proceedings of the National Academy of Sciences, USA,***113**No. 10 (2016), pages 2603-2608. -
Explorations in the theory of partition zeta functions
*(with Larry Rolen and Robert Schneider),*Exploring the Riemann Zeta-function - 190 years from Riemann's Birth (Ed. H. Montgomery, A. Nikeghbali, and M. Rassias), Springer, New York, 2017, pages 223-264. -
Zeta-polynomials for modular form periods
*(with Larry Rolen and Florian E. Sprung),**Advances in Mathematics,***306**No. 14 (2017), pages 328-343. -
Why Ramanujan matters,
*(with Robert Schneider)**Science and Film,*May 10, 2016. - The Man Who Knew Infinity: Why Ramanujan Matters
*(with Robert Schneider),**Ramanujan Mathematical Society Newsletter,*Volume 26, March-June 2016 Issue, pages 109-110. - On Divisors of modular forms
*(with Kathrin Bringmann, Ben Kane, Steffen Löbrich, and Larry Rolen),**Advances in Mathematics,***329**, (2018), 541-554. -
Why Ramanujan matters,
*(with Robert Schneider)**Asia Pacific Mathematics Newsletter,***6**, December 2016, pages 27-28. -
Number-theoretic generalization of the Monster denominator formula,
*(with Kathrin Bringmann, Ben Kane, Steffen Löbrich, and Larry Rolen)*,*Journal of Physics A,***50**(2017), 473-501. -
O'Nan Moonshine and Arithmetic
*(with John Duncan and Michael Mertens)*,*American Journal of Mathematics*, accepted for publication. - Partition-theoretic formulas for arithmetic densities,
*(with Robert Schneider and Ian Wagner)*,

Proceedings of Number Theory in honor of Krishna Alladi's 60th birthday, Springer, Springer Proc. Math. Stat.**221**, 2017, 611-624. - Review of "The G. H. Hardy Reader",

The Hardy-Ramanujan Journal,**40**(2017), 43-46. - Pariah Moonshine,
*(with John Duncan and Michael Mertens)**Nature*, Ser. Communications,**8**(2017), Art. 670. - Mentoring Graduate Students,
*Notices of the American Mathematical Society,*to appear. - A word from the Vice President,
*Notices of the American Mathematical Society,***66**(2019), 466. - CM evaluations of the Goswami-Sun series
*(with Madeline Locus Dawsey),**Proceedings of a Conference on Elliptic curves at Zeuthen,*(Ed. J. Blumlein, et al.) Springer, 2019, 183-193. -
On Witten's extremal partition functions
*(with Larry Rolen),*(In Honor of George Andrews),*Annals of Combinatorics,*accepted for publication. - Black holes and class groups,
*(with Nathan Benjamin, Shamit Kachru, and Larry Rolen)*,*Research in the Mathematical Sciences*,**5**(2018), A43. -
Higher width Moonshine
*(with Madeline Locus Dawsey),*submitted for publication. -
Jensen polynomials for Riemann's zeta function and suitable arithmetic
sequences
*(with Michael Griffin, Larry Rolen, and Don Zagier)*,

Proceedings of the National Academy of Sciences, USA, (Online first: www.pnas.org/cgi/doi/10.1073/pnas.1902572116). - Seeking speed with sensors
*(with Madeline Locus Dawsey),*Splash, in press. - Partitions to Hodge numbers of Hilbert schemes of surfaces
*(with Nate Gillman, Xavier Gonzalez, Larry Rolen, and Matthew Schoenbauer)*, submitted for publication. - Multiquadratic fields generated by characters of
*A_n**(with Madeline Locus Dawsey and Ian Wagner)*,

Journal of Algebra, recommended for publication. - Case study of elite breaststrokers using inertial measurement units
*(with Jon Howell, Sven Mesihovic, Fiona Muir, Sage Ono, and Larry Rolen)*, submitted for publication. - To be determined
*(with Michael Mertens and Larry Rolen)*, in preparation. - To be determined
*(with Madeline Locus Dawsey and Ian Wagner)*, in preparation. - To be determined
*(with Michael Griffin and Jesse Thorner)*, in preparation.