## REUs Archive: 2013

### Research Experiences for Undergraduates at Emory University

**Number Theory**

### 2013 Research Experiences for Undergraduates at Emory University

**Number Theory**

#### Dates: June 3, 2013- July 26, 2013

#### Math Building, Room E406

#### Instructors

- David Zureick-Brown, Assistant Professor.
- Ken Ono, Asa Griggs Candler Professor.
- Robert Lemke Oliver,NSF postdoc (Stanford)
- Larry Rolen,NSF Graduate Fellow, (Emory)

#### 2013 Project areas

- Elliptic curves and Galois representations
- Mock modular and quantum modular forms
- Additive Number Theory
- Distribution of Primes

#### Participants

- Ping Ngai (Brian) Chung (MIT)
- Eric Larson* (Harvard): 2014 Frank and Brennie Morgan Prize Winner
- Hannah Larson* (S. Eugene High School): 2013 Davidson Fellow
- Shiyu Li (UC Berkeley): 2014 Honorable Mention for Schafer Prize
- Akhil Mathew (Harvard)
- Sarah Peluse (U. Chicago): 2014 Schafer Prize Winner
- Sarah Pitman (Emory U.)
- Jesse Silliman (U. Chicago)
- Geoffrey Smith (Yale): Goldwater Scholar
- Isabel Vogt (Harvard)

Note. Special participant.

#### Their results

- Ping Ngai (Brian) Chung and Shiyu Li,
On the residue classes of pi(n) modulo t, Integers,
**13**(2013), A79. - Ping Ngai (Brian) Chung and Shiyu Li,
Bounded gaps between products of special primes,
Mathematics,
**2**(2014), pages 37-52. - Hannah Larson and Geoffrey Smith, Congruence properties of Taylor coefficients of modular forms,
International Journal of Number Theory,
**10**(2014), pages 1501-1518. - Sarah Peluse, Irreducible representations of
*SU(n)*with prime power degree, Seminaire Lotharingien de Combinatoire**71**(2013/14), Art. B71d. - Sarah Peluse, On zeros of Eichler integrals, Archiv der Mathematik,
**102**(2014), pages 71-81. - Sarah Pitman,
*3F2*-hypergeometric functions and supersingular elliptic curves, Involve,**8**(2015), pages 481-490. - Jesse Silliman and Isabel Vogt, Powers in Lucas sequences via Galois representations, Proceedings of the American Mathematical Society,
**143**(2015), pages 1027-1041.

#### Application Materials (applications no longer accepted)

A completed application consists of an application form , personal statement, two letters of recommendation, and current transcripts. These materials should be sent to:

Ken Ono

Department of Mathematics and Computer Science

Emory University

400 Dowman Drive

Atlanta, Georgia 30322