Fourier coefficients of Eisenstein series and applications

Abstract: A classical topic in modular forms is the computation of the Fourier coefficients of the Eisenstein series for GL(2). Computing the Fourier coefficients of Eisenstein series on higher rank groups has been more difficult. I will describe a method to do this computation in some new cases: for certain Eisenstein series on groups of type D_4, F_4, and E_n. I will also describe some arithmetic applications, including to solving an "exceptional" counting problem. This is joint work in progress with Bryan Hu, Jennifer Johnson-Leung, Finn McGlade, and Manami Roy.

number theoryrepresentation theory

Audience: researchers in the topic

University of Utah Representation Theory / Number Theory Seminar