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SUMMARY:Peter Humphries (University of Virginia)
DTSTART:20220317T213000Z
DTEND:20220317T223000Z
DTSTAMP:20260423T024721Z
UID:JNTS/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JNTS/39/">Sp
 ectral reciprocity and applications</a>\nby Peter Humphries (University of
  Virginia) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstrac
 t\nSpectral reciprocity is a phenomenon in which certain moments of L-func
 tions are shown to be exactly equal to other moments of L-functions. A qui
 ntessential example is Motohashi's formula\, which relates the fourth mome
 nt of the Riemann zeta function to the third moment of L-functions associa
 ted to GL(2) automorphic forms. I will discuss generalisations of Motohash
 i's formula\, how to prove these formulae using tools from the theory of a
 utomorphic forms\, and applications of these formulae to problems in analy
 tic number theory\, including the $L^4$-norm problem for automorphic forms
 .\n
LOCATION:https://researchseminars.org/talk/JNTS/39/
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