Eulerianity of Fourier coefficients of automorphic forms

Eulerianity of Fourier coefficients of automorphic forms

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Henrik Gustafsson, IAS

Zoom link:

https://theias.zoom.us/j/959183254

Password: the three digit integer that is the cube of the sum of its digits

The factorization of Fourier coefficients of automorphic forms plays an important role in a wide range of topics, from the study of L-functions to the interpretation of scattering amplitudes in string theory.

In this talk I will present a transfer theorem which derives the Eulerianity of certain Fourier coefficients from that of another coefficient. I will also discuss some applications of this theorem to Fourier coefficients of automorphic forms in minimal and next-to-minimal representations.

Based on recent work with Dmitry Gourevitch, Axel Kleinschmidt, Daniel Persson and Siddhartha Sahi.