Ken Ono

Asa Griggs Candler Professor of Mathematics

Department of Mathematics and Computer Science
Emory University

Publications

  1. Shimura sums related to quadratic imaginary fields
    Proceedings of the Japan Academy of Sciences 70(A), No. 5, 1994, pp. 146-151
  2. Congruences on the Fourier coefficients of modular forms on Γ0(N)
    The Rademacher Legacy to Mathematics, Contemporary Mathematics 166, 1994, pp. 93-105
  3. On the positivity of the number of partitions that are t-cores
    Acta Arithmetica 66, No. 3, 1994, pp. 221-228
  4. Superlacunary cusp forms (with Sinai Robbins)
    Proceedings of the America Mathematical Society 123, No. 4, 1995, pp. 1021-1029
  5. Parity of the partition function
    Electronic Research Announcements of the American Mathematical Society 1, No. 1, 1995, pp. 35-42
  6. On the representation of integers as sums of triangular number (with Sinai Robbins and Patrick Wahl)
    Aequationes Mathematica 50, 1995, pp. 73-94
  7. A note on the number of t-core partitions
    The Rocky Mountain Journal of Mathematics 25, No. 3, 1995, pp. 1165-1169
  8. A note on the Shimura correspondence and the Ramanujuan τ(n) function
    Utilitas Mathematica 47, 1995, pp. 170-180
  9. Congruences for Frobenius partitions
    Journal of Number Theory 57, No. 1, 1996, pp. 331-347
  10. Defect zero p-blocks for finite simple groups (with Andrew Granville)
    Transactions of the American Mathematical Society 348, No. 1, 1996, pp. 331-347
  11. On the parity of the partition function in arithmetic progressions
    Journal fur die reine und angewandte Mathematik 472, 1996, pp. 1-15
  12. 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
  13. Congruences for partition functions (with Dennis Eichlorn)
    Proceedings for a Conference in Honor of Heini Halbertstam 1, 1996, pp, 309-321
  14. Rank zero quadratic twists of modular elliptic curves
    Compositio Mathematica 104, 1996, 293-304
  15. Quadratic forms and elliptic curves III (with Takashi Ono)
    Proceedings of the Japan Academy of Sciences 72(A), 1996, pp. 204-205
  16. Euler's concordant forms
    Acta Arithmetica 65, 1996, pp. 101-123
  17. Some recurrences for arithmetical functions (with Neville Robbins and Brad Wilson)
    Journal of the Indian Mathematical Society 62, 1996, pp, 29-50
  18. Divisibility properties of certain partition functions by powers of primes (with Basil Gordon)
    The Ramanujan Journal 1, 1997, pp, 25-35
  19. Parity of the Fourier coefficients of modular forms (with Brad Wilson)
    Illinois Journal of Mathematics 41, 1997, pp. 142-150
  20. Odd values of the partition function
    Discrete Mathematics 169, 1997, pp. 263-268
  21. 4-core partitions and class numbers (with Lawrence Sze)
    Acta Arithmetica 65, 1997, pp. 249-272
  22. Twists of elliptic curves
    Compositio Mathematica 106, 1997, pp. 349-360
  23. Ramanujan, taxicabs, birthdates, zipcodes and twists
    American Mathematical Monthly 104, No. 10, 1997, pp. 912-917
  24. Tate-Shafarevich groups of the congruent number elliptic curves
    Acta Arithmetica 81, 1997, pp. 247-252
  25. Ramanujan's ternary quadratic form (with Soundararajan Kannan)
    Inventiones Mathematicae 130, No. 3, 1997, pp. 415-454
  26. Eta-quotients and elliptic curves (with Yves Martin)
    Proceedings of the American Mathematical Society 125, 1997, pp. 3169-3176
  27. Values of Gaussian hypergeometric series
    Transactions of the American Mathematical Society 350, No. 3, 1998, pp. 1205-1223
  28. 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
  29. Fourier coefficients of half-integral weight modular forms modulo l (with Chris Skinner)
    Annals of Mathematics 147, No. 2, 1998, pp. 453-470
  30. 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
  31. Partitions into distinct parts and elliptic curves
    Journal of Combinatorial Theory 82(A), 1998, pp. 193-201
  32. 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
  33. The residue of p(n) modulo small primes
    Erdos Memorial Issue, The Ramanujan Journal 2, 1998, pp, 47-54
  34. The partition function in arithmetic progressions
    Mathematische Annalen 312, 1998, pp, 251-260
  35. Rook theory and t-cores (with Jim Haglund and Lawrence Sze)
    Journal of Combinatorial Theory 84(A), 1998, pp. 9-37
  36. 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
  37. Nonvanishing of quadratic twists of modular L-functions (with Chris Skinner)
    Inventiones Mathematicae 134, 1998, pp. 651-660
  38. Integers represented by ternary quadratic forms (with Soundararajan Kannan)
    Proceedings of the 5th Meeting of the Canadian Number Theory Association, CRM Proceedings and Lecture Notes 19, 1998, pp. 527-532
  39. A note on the irreducibility of Hecke polynomials (with Kevin James)
    Journal of Number Theory 73, 1998, pp. 527-532
  40. 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
  41. 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
  42. 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
  43. Selmer groups of quadratic twists of modular elliptic curves (with Kevin James)
    Mathematische Annalen 314, 1999, pp. 1-17
  44. 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
  45. On the circular summation of the eleventh powers of Ramanujan's theta function
    Journal of Number Theory 76, 1999, pp. 62-65
  46. Indivisibility of class numbers of real quadratic fields
    Compositio Mathematica 119, 1999, pp. 1-11
  47. The partition function and the arithmetic of certain modular L-functions (with Li Guo)
    International Mathematical Research Notices, 1999, No. 21, pp. 1179-1197
  48. Distribution of the partition function modulo m
    Annals of Mathematics 151, 2000, pp. 293-307
  49. A Gaussian hypergeometric series evaluation and Apery number congruences (with Scott Ahlgren)
    Journal fur die reine und angewandte Mathematik 518, 2000, pp. 187-212
  50. Modularity of a certain Calabi-Yau threefold (with Scott Ahlgren)
    Monatshefte fur Mathematik 129, 2000, pp. 177-190
  51. On "good" half-integral weight modular forms (with Jorge Jimenez-Urroz)
    Mathematics Research Letters 7, No. 2, 2000, pp. 205-212
  52. 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
  53. 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
  54. Differential endomorphisms for modular forms on Γ0(4)
    Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, (eds.) F. Garvan, M. Ismail, Kluwer Academic Publishers, 1999, pp. 223-230
  55. q-series identities and values of certain L-functions (with George Andrews and Jorge Jimenez-Urroz)
    Duke Mathematical Journal 108, 2001, pp. 395-419
  56. 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
  57. 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
  58. Addition and counting: The arithmetic of partitions (with Scott Ahlgren)
    Notices of the American Mathematical Society 48, October 2001, pp. 978-984
  59. 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
  60. 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
  61. Congruence properties for the partition function (with Scott Ahlgren)
    Proceedings of the National Academy of Sciences, USA, 98, Issue 23, 2001, pp. 12882-12884
  62. The Chebotarev density theorem in short intervals and some questions of Serre (with Antal Balog)
    Journal of Number Theory 91, 2001, pp. 356-371
  63. 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
  64. 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
  65. Zeta functions of an infinite family of K3 surfaces (with Scott Ahlgren and David Penniston)
    American Journal of Mathematics 124, 2002, pp. 353-368
  66. Representations of integers as sums of squares
    Journal of Number Theory 95, 2002, pp. 253-258
  67. 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
  68. 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
  69. Congruences for 3F2 hypergeometric functions over finite fields (with David Penniston)
    Illinois Journal of Mathematics 46, 2002, pp. 679-684
  70. Weierstrass points on X0(p) and supersingular j-invariants (with Scott Ahlgren)
    Mathematiche Annalen 325, 2003, pp. 355-368
  71. Coefficients of half-integral weight modular forms (with Jan Bruinier)
    Journal of Number Theory 99, 2003, pp. 164-179
  72. Modular form congruences and Selmer groups (with William McGraw)
    Journal of the London Mathematical Society 67, 2003, pp. 302-318
  73. Arithmetic of the coefficients of Cohen's Eisenstein series (with Antal Balog and William McGraw)
    Acta Arithmetica 107, 2003, pp. 337-344
  74. 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
  75. Baxter algebras and Hopf algebras (with George Andrews, Li Guo, William Keigher)
    Transactions of the American Mathematical Society 355, 2003, pp. 4639-4656
  76. The life and work of R.A. Rankin (with Bruce Berndt and Winfried Kohnen)
    The Ramanujan Journal 7, 2003, pp. 11-40
  77. Elements of class groups and Shafarevich-Tate groups of elliptic curves (with Antal Balog)
    Duke Mathematical Journal 120, 2003, pp. 35-63
  78. Arithmetic of Borcherds' exponents (with Jan Bruinier)
    Mathematische Annalen 327, 2003, pp. 293-303
  79. 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
  80. 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.
  81. Arithmetic of certain hypergeometric modular forms (with Karl Mahlburg)
    Acta Arithmetica 113, 2004, pp. 39-55.
  82. Hecke operators and the q-expansion of modular forms
    Proceedings of the 7th Meeting of the Canadian Number Theory Association, Montreal 2002, CRM Conference Proceedings and Lecture Notes 36, 2004, American Mathematical Society, pp. 229-235.
  83. Arithmetic of singular moduli and class polynomials (with Scott Ahlgren)
    Compositio Mathematica, 141, 2005, pp. 293-312.
  84. Gaussian hypergeometric functions and Hecke operators (with Sharon Frechette and Matt Papanikolas)
    International Mathematical Research Notices, 60, 2004, pp. 3233-3262.
  85. 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
  86. 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.
  87. Partitions and McKay numbers for Sn ,
    Journal of Combinatorial Theory, Series A, 108, 2004, pages 185-197.
  88. 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.
  89. 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.
  90. Hilbert class polynomials and traces of singular moduli (with Jan Bruinier and Paul Jenkins),
    Mathematische Annalen, 334 no. 2, 2006, pages 373-393.
  91. 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.
  92. 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.
  93. Identities for traces of singular moduli (with Kathrin Bringmann),
    Acta Arithmetica, 119 (2005), pages 317-327.
  94. 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.
  95. Traces of singular moduli on Hilbert modular surfaces (with Kathrin Bringmann and Jeremy Rouse),
    International Mathematical Research Notices, 47 (2005), pages 2891-2912.
  96. Arithmetic properties of coefficients of half-integral weight Maass-Poincare series (with Kathrin Bringmann),
    Mathematische Annalen, 337 (2007), pages 591-612.
  97. An arithmetic formula for the partition function (with Kathrin Bringmann),
    Proceedings of the American Mathematical Society, 135 (2007), pages 3507-3514.
  98. The $f(q)$ mock theta function conjecture and partition ranks (with Kathrin Bringmann),
    Inventiones Mathematicae, 165 (2006), pages 243-266.
  99. 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.
  100. Dyson's ranks and Maass forms, (with Kathrin Bringmann),
    Annals of Mathematics, 171 (2010), pages 419-449.
  101. Ramanujan's congruences and Dyson's crank (with George Andrews),
    Proceedings of the National Academy of Sciences, USA, 102, No. 43 (2005), page 15277.
  102. Mock theta functions, ranks, and Maass forms, Surveys in Number Theory, Developments in Mathematics (Ed. K. Alladi) 17, Springer-Verlag, 2008, pages 119-142.
  103. Honoring a gift from Kumbakonam,
    Notices of the American Mathematical Society, 53, Number 6 (2006), pages 640-651.
  104. Divisibility criteria for class numbers of imaginary quadratic fields, (with Paul Jenkins),
    Acta Arithmetica, 125 (2006), pages 285-289.
  105. q-series and weight 3/2 Maass forms (with Kathrin Bringmann and Amanda Folsom),
    Compositio Mathematica, 145 (2009), pages 541-552.
  106. 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.
  107. Duality involving the mock theta function f(q) (with Amanda Folsom),
    Journal of the London Mathematical Society, 77 (2008), pages 320-334.
  108. Eulerian series as modular forms (with Kathrin Bringmann and Rob Rhoades),
    Journal of the American Mathematical Society, 21 (2008), pages 1085-1104.
  109. Heegner divisors, L-functions, and Maass forms (with Jan H. Bruinier),
    Annals of Mathematics, 172 (2010), pp. 2135-2181.
  110. Algebraicity of harmonic Maass forms,
    SASTRA Prize volume, Ramanujan Journal, 20 (2009), pages 297-309.
  111. 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.
  112. 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.
  113. 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.
  114. 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.
  115. 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.
  116. 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.
  117. Hook lengths and 3-cores, (with Guo-Niu Han),
    Annals of Combinatorics, 15 (2011), pages 305-312.
  118. SO(3)-Donaldson invariants of CP^2 and mock theta functions, (with Andreas Malmendier), Geometry and Topology, 16 (2012), pages 1767-1833.
  119. 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.
  120. Lehmer's conjecture on Ramanujan's tau-function,
    Journal of the Indian Mathematical Society, (2008), Special Centenary Issue, pages 149-163.
  121. Probabilities as values of modular forms and continued fractions (with Riad Masri),
    International Journal of Mathematics and the Mathematical Sciences, (2009), Article ID 941920.
  122. Some characters of Kac and Wakimoto and nonholomorphic modular functions (with Kathrin Bringmann),
    Mathematische Annalen, 345 (2009), pages 547-558.
  123. Identities and congruences for the coefficients of Ramanujan's omega(q) (with Jan H. Bruinier), Ramanujan Journal 23 (2010), pages 151-157.
  124. 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.
  125. 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.
  126. The parity of the partition function,
    Advances in Mathematics, 225 (2010), pages 349-366.
  127. The last words of a genius,
    Notices of the American Mathematical Society,57 (2010), pages 1410-1419.
  128. Gauss's 2F1 hypergeometric function and the congruent number elliptic curve, (with Ahmad El-Guindy),
    Acta Arithmetica, 144 (2010), pages 231-239.
  129. Hasse invariants for the Clausen elliptic curves, (with Ahmad El-Guindy), Ramanujan Journal, 31 (2013), pages 3-13.
  130. Eichler-Shimura theory for mock modular forms, (with Kathrin Bringmann, Pavel Guerzhoy, and Zach Kent),
    Mathematische Annalen, 355 (2013), pages 1085-1121.
  131. Congruences for the Andrews spt-function, Proceedings of the National Academy of Sciences, USA, 108 (2011), pages 473-476.
  132. The partition function and Hecke operators, Advances in Mathematics, 228 (2011), pages 527-534.
  133. l-adic properties of the partition function (with Amanda Folsom and Zach Kent),
    Advances in Mathematics, 229 (2012), pages 1586-1609.
  134. Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms (with Jan Bruinier),
    Advances in Mathematics, 246 (2013), pages 198-219.
  135. A mod l Atkin-Lehner theorem and applications (with Nick Ramsey), Archiv der Mathematik, 98 (2012), pages 25-36 (Birkhauser-Verlag Distinguished Article).
  136. 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.
  137. SU(2) Donaldson invariants of the projective plane, (with Michael Griffin and Andreas Malmendier), Forum Mathematicum, 27 (2015), pages 2003-2023.
  138. ``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.
  139. 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.
  140. 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.
  141. Moonshine for M24 and Donaldson invariants for CP^2, (with Andreas Malmendier) Communications in Number Theory and Physics, 6 (2012), pages 759-770.
  142. Mock theta functions and quantum modular forms, (with Amanda Folsom and Rob Rhoades)
    Forum of Mathematics, Pi, 1 (2013), e2, 27 pages.
  143. 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.
  144. 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.
  145. 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.
  146. Weierstrass mock modular forms and elliptic curves, (with Claudia Alfes, Michael Griffin and Larry Rolen), Research in Number Theory, 1: 24 (2015).
  147. 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..
  148. 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.
  149. Maximal multiplicative properties of partitions (with Christine Bessenrodt),
    Annals of Combinatorics, 20 (2016), pages 59-64.
  150. Special values of shifted convolution Dirichlet series (with Michael Mertens),
    Mathematika, 62 (2016), pages 47-66.
  151. Moonshine (with John F. R. Duncan and Michael Griffin),
    Research in the Mathematical Sciences, 2 (2015), A11.
  152. 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.
  153. Proof of the Umbral Moonshine Conjecture (with John F. R. Duncan and Michael Griffin),
    Research in the Mathematical Sciences, 2: 26 (2015).
  154. The Jack Daniels Problem (with John F. R. Duncan), Winnie Li Special Issue of Journal of Number Theory, 161 (2016), pages 230-239.
  155. The 1729 K3 surface (with Sarah Trebat Leder),
    Research in Number Theory, 2 (2016), 2: 26.
  156. A note on nonordinary primes (with Seokho Jin and Wenjun Ma),
    Proceedings of the American Mathematical Society, 144 (2016), pages 4591-4597.
  157. 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.
  158. 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, accepted for publication.
  159. Zeta-polynomials for modular form periods (with Larry Rolen and Florian E. Sprung),
    Advances in Mathematics, 306 No. 14 (2017), pages 328-343.
  160. Why Ramanujan matters, (with Robert Schneider)
    Science and Film, May 10, 2016.
  161. The Man Who Knew Infinity: Why Ramanujan Matters (with Robert Schneider),
    Ramanujan Mathematical Society Newsletter, Volume 26, March-June 2016 Issue, pages 109-110.
  162. On Divisors of modular forms (with Kathrin Bringmann, Ben Kane, Steffen Löbrich, and Larry Rolen), submitted for publication.
  163. Why Ramanujan matters, (with Robert Schneider)
    Asia Pacific Mathematics Newsletter, 6, December 2016, pages 27-28.
  164. Number-theoretic generalization of the Monster denominator formula, (with Kathrin Bringmann, Ben Kane, Steffen Löbrich, and Larry Rolen),
    Journal of Physics A, accepted for publication.
  165. O'Nan Moonshine and Arithmetic (with John Duncan and Michael Mertens) , submitted for publication.
  166. 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, accepted for publication.
  167. Review of "The G. H. Hardy Reader",
    The Hardy-Ramanujan Journal, in press.
  168. Pariah Moonshine, (with John Duncan and Michael Mertens)
    Nature, Ser. Communications, accepted for publication.