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CATEGORIES:Number Theory Seminar
SUMMARY:Fourier coefficients of Siegel modular forms and a
pplications - Abhishek Saha (University of Bristol
)
DTSTART;TZID=Europe/London:20160119T141500
DTEND;TZID=Europe/London:20160119T151500
UID:TALK62999AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/62999
DESCRIPTION:The Fourier coefficients of classical modular form
s essentially coincide (in the case of Hecke eigen
forms) with their Hecke eigenvalues\, or equivalen
tly\, with the coefficients of the associated L-fu
nction. The situation is very different for Siegel
modular forms of degree 2. The Fourier expansion
now contains substantial information beyond the He
cke eigenvalues. Indeed\, a remarkable conjecture
of Bocherer predicts that certain averages of thes
e Fourier coefficients are essentially linked to t
wisted central values of spinor L-functions. In th
is talk\, I will discuss some precise refinements
of this conjecture and its relation with the globa
l Gan-Gross-Prasad conjecture as refined by Ichino
-Ikeda and Liu. I will also describe several appli
cations 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 Pit
ale and Ralf Schmidt.
LOCATION:MR13
CONTACT:Jack Thorne
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