Spring 2025

MATH GR8675 TOPICS IN NUMBER THEORY

Instructor: Dorian Goldfeld
Day/Time: TR 02:40 – 03:55PM
Title: Analytic Number Theory
Abstract: This course will focus on the spectral theory of cusp forms and Langlands Eisenstein series for the group SL(n,Z) for n > 2. Using trace formula techniques we will obtain applications to classical problems in analytic number theory such as, subconvexity bounds and densities of low lying zeros of Godement-Jacquet L-functions, Siegel zeros, vertical Sato-Tate distributions, asymptotic orthogonality relations for eigenvalues of Hecke operators, as well as more modern developments such as spectral reciprocity and the theory of arithmetic murmurations.

https://doc.sis.columbia.edu/#subj/MATH/G8675-20251-001/

Print this page