Fourier coefficients of Siegel modular forms and applications

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• Abhishek Saha (University of Bristol)
• Tuesday 19 January 2016, 14:15-15:15
• MR13.

If you have a question about this talk, please contact Jack Thorne.

The Fourier coefficients of classical modular forms essentially coincide (in the case of Hecke eigenforms) with their Hecke eigenvalues, or equivalently, with the coefficients of the associated L-function. The situation is very different for Siegel modular forms of degree 2. The Fourier expansion now contains substantial information beyond the Hecke eigenvalues. Indeed, a remarkable conjecture of Bocherer predicts that certain averages of these Fourier coefficients are essentially linked to twisted central values of spinor L-functions. In this talk, I will discuss some precise refinements of this conjecture and its relation with the global Gan-Gross-Prasad conjecture as refined by Ichino-Ikeda and Liu. I will also describe several applications of these refined results to non-vanishing, algebraicity and integrality of central L-values of cohomological automorphic forms on GL(2), via a lifting argument from GL(2) to GSp(4). Part of this is joint work with Martin Dickson, Ameya Pitale and Ralf Schmidt.

This talk is part of the Number Theory Seminar series.

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