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Average values of Rankin-Selberg L-functions for GL(2)

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Speaker: 
Jeanine Van Order
Affiliation: 
The Hebrew U of Jerusalem/MPI
Date: 
Wed, 24/09/2014 - 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar
I will discuss some techniques to estimate central values of Rankin-Selberg
L-functions for GL(2) in the self-dual setting, and in particular how a
trick from the spectral theory of automorphic forms can be used to reduce
the problem to a suitable application of the approximate functional
equation method. This work is motivated both by applications to bounding
(or else showing systematic growth of) Mordell-Weil ranks of abelian
varieties in certain abelian extensions of CM fields (not conditional on
the conjecture of Birch and Swinnerton-Dyer), as well as to folklore
conjectures for higher-rank groups which might eventually be accessible by
similar techniques. I will explain both of these motivations if time
permits.
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