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SUMMARY:Elad Zelingher (Yale University)
DTSTART:20220510T210000Z
DTEND:20220510T220000Z
DTSTAMP:20260423T010004Z
UID:UAANTS/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/43/">
 On regularization of integrals of matrix coefficients associated to spheri
 cal Bessel models</a>\nby Elad Zelingher (Yale University) as part of Univ
 ersity of Arizona Algebra and Number Theory Seminar\n\n\nAbstract\nThe Gan
 -Gross-Prasad conjecture relates a special value of an L-function of two c
 uspidal automorphic representations to the non-vanishing of a certain peri
 od. The Ichino-Ikeda conjecture is a refinement of this conjecture. It rou
 ghly states that the absolute value of the square of the period in questio
 n can be expressed as a product of the special value of the L-function and
  a product of normalized local periods. However\, in order to formulate th
 is conjecture\, one needs to assume that the representations in question a
 re tempered everywhere\, or else the convergence of the local periods is n
 ot guaranteed. The generalized Ramanujan conjecture speculates that the re
 presentations in question (cuspidal automorphic representations lying in g
 eneric packets) are already tempered everywhere. However\, the generalized
  Ramanujan conjecture is far from being known. In this talk\, I will expla
 in how to drop the assumption that the representations are tempered almost
  everywhere. I will explain how to extend the definition of the normalized
  local periods for places where the local components are given by principa
 l series representations.\n
LOCATION:https://researchseminars.org/talk/UAANTS/43/
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