# Number Theory Student Seminar at Ohio State

In Fall 2021, the number theory student seminar will meet bi-weekly on Tuesday from 6:30PM-7:30PM via Zoom.

Here is the webpage for previous number theory student seminar.

Current organizers: Joseph Leung (leung.179@osu.edu), Julian Mejia Cordero (mejiacordero.2@osu.edu), Pan Yan (yan.669@osu.edu)

## Schedule:

### November 23, 6:30PM-7:30PM

Speaker: Joseph Leung

Title: A New Variant of the Delta Method and Subconvexity

Abstract: The Delta method have been a popular tool in analytic number theory in recent years, due to several successful attempts in establishing nontrivial bounds in settings such as subconvexity problems. In this talk, I am going to first introduce what the Delta method is and the basic philosophy behind its application. Then I will introduce the classical choices of the delta method followed by a new variant of the Delta method, and compare their differences. Finally, I will talk about the 'standard' way to tackle subconvexity problems using the Delta method, with the hybrid subconvexity problem of $L(1/2, \text{sym}^2 f \otimes g)$ in mind.

### October 12, 6:30PM-7:30PM

Speaker: Zhining Wei

Title: Linear Relations of Siegel Poincare Series and Non-vanshing of the Central Values of Spinor L-functions

Abstract: In this paper, we will first investigate the linear relations of a one parameter family of Siegel Poincar\'e series. Then we give the applications to the non-vanishing of Fourier coefficients of Siegel cusp eigenforms and the central values.

### September 28, 6:30PM-7:30PM

Speaker: Jake Huryn

Abstract: Kummer gave a necessary and sufficient condition for the p-part of the class group of the pth cyclotomic field to be trivial. We discuss a refinement of Kummer’s criterion, the Herbrand–Ribet theorem, and its connections to other parts of number theory, such as modular forms, Galois representations, and Iwasawa theory.