Stanford University

Stanford, California

**Email: jthorner@stanford.edu**

**Address:Department of MathematicsStanford University Building 380Stanford, CA 94305**

I am a NSF Postdoctoral Fellow at Stanford University working with Kannan Soundararajan .

My research interests lie in number theory. I use analytic methods to study automorphic forms, elliptic curves, L-functions, modular forms, and the distribution of primes.

I graduated with distinction from Duke University in 2009 with a BS in Mathematics. I completed by MA in mathematics at Wake Forest University in 2013 ; my advisor was Jeremy Rouse. I completed my Ph.D. in mathematics at Emory University in 2016; my advisor was Ken Ono.

Here is my CV.

14. The GL(n) large sieve (with Asif Zaman), submitted.

13. Zeros of Rankin-Selberg L-functions at the edge of the critical strip (with Farrell Brumley and Asif Zaman), submitted.

12.
Weak subconvexity without a Ramanujan hypothesis (with Kannan Soundararajan), Duke Math. J. **168** (2019), no. 7, 1231-1268. Appendix by Farrell Brumley.

11. A unified and improved Chebotarev density theorem (with Asif Zaman), Algebra Number Theory, accepted for publication.

10.
Special Values of Motivic L-Functions and Zeta-Polynomials for Symmetric Powers of Elliptic Curves (with Steffen Lobrich and Wenjun Ma), Res. Math. Sci. **4** (2017) Paper No. 26, 16 pp.

9. A Chebotarev variant of the Brun-Titchmarsh theorem and bounds for the Lang-Trotter conjectures (with Asif Zaman), to appear in Int. Math. Res. Not.

8.
An explicit bound for the least prime ideal in the Chebotarev density theorem (with Asif Zaman), Algebra Number Theory **11** (2017), no. 5, 1135-1197.

7. Bounded gaps between primes in multidimensional Hecke equidistribution problems, to appear in Math. Res. Lett.

6. Effective log-free zero density estimates for automorphic L-functions and the Sato-Tate Conjecture (with Robert Lemke Oliver), to appear in Int. Math. Res. Not.

5.
Benford's law for coefficients of newforms (with Marie Jameson and Lynnelle Ye), Int. J. Number Theory **12** (2016), no. 2, 483-494

4.
On the error term in the Sato-Tate conjecture. Arch. Math. **103** (2014), 147-156.

3.
A variant of the Bombieri-Vinogradov theorem for short intervals and some questions of Serre. Math. Proc. Cambridge Philos. Soc. **161** (2016), no. 1, 53-63.

2.
Bounded gaps between primes in Chebotarev sets. Res. Math. Sci. 2014 **1**:4.

1.
The explicit Sato-Tate conjecture and densities pertaining to Lehmer-type questions (with Jeremy Rouse), Trans. Amer. Math. Soc. **369** (2017), no. 5, 3575-3604.

Spring 2019, Stanford University, Math 115 Course Instructor (Functions of a Real Variable)

Fall 2018, Stanford University, Math 115 Course Instructor (Functions of a Real Variable)

Spring 2018, Stanford University, Math 109 Course Instructor (Applied Group Theory)

Spring 2018, Stanford University, Math 155 Course Instructor (Analytic Number Theory)

Spring 2016, Emory University, Math 112 Course Instructor (Integral Calculus), Section 5

Fall 2015, Emory University, Math 111 Course Instructor (Differential Calculus), Sections 1 and 2

Spring 2015, Emory University, Math 111 Course Instructor (Differential Calculus), Section 5