# Number Theory Student Seminar

This is the home of the OSU Number Theory Student Seminar. We hope to cover topics/techniques/papers of interest in both analytic and algebraic number theory, particularly those that may not be covered in the number theory course sequence. We welcome all who would like to attend.

For the Spring 2018 semester, we will meet every other Tuesday at 5:30PM in MW 154, unless otherwise noted. If you are interested in giving a talk, or would like to be added to the mailing list, please contact Alex Beckwith at beckwith.67 (at) osu (dot) edu.

## Upcoming talk

• 20 February: Yongxiao Lin

Title: Titchmarsh's Argument for Bounding the Epstein Zeta Function (click for abstract)

Abstract: We will describe Titchmarsh's strategy, based on van der Corput's method, for bounding the Epstein zeta function. By using Weyl differencing, a two-dimensional second derivative test, Titchmarsh (1934) proved a bound $E\left(\frac{1}{2}+it\right)=O\left(t^{\frac{1}{3}}\log^3 t\right)$, for a particular instance of the Epstein zeta function, $$E(s):=\sum\sum_{(m,n)\in \mathbb{Z}^2\backslash (0,0)} Q(m,n)^{-s},$$ where $Q(m,n)=m^2+an^2$ ($a>0$). This is comparable to the classical bound $\zeta\left(\frac{1}{2}+it\right)=O\left(t^{\frac{1}{6}}\log t\right)$ for the Riemann zeta function $\zeta(s)$. If time permits, we will mention briefly recent generalizations of V. Blomer, and of D. Schindler, based on Titchmarsh's argument.