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SUMMARY:Fourier coefficients of Siegel modular forms and applications - Ab
 hishek Saha (University of Bristol)
DTSTART:20160119T141500Z
DTEND:20160119T151500Z
UID:TALK62999@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:The Fourier coefficients of classical modular forms essentiall
 y coincide (in the case of Hecke eigenforms) with their Hecke eigenvalues\
 , or equivalently\, with the coefficients of the associated L-function. Th
 e situation is very different for Siegel modular forms of degree 2. The Fo
 urier expansion now contains substantial information beyond the Hecke eige
 nvalues. Indeed\, a remarkable conjecture of Bocherer predicts that certai
 n 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 Ga
 n-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 automorp
 hic 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.
LOCATION:MR13
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