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SUMMARY:Paul Nelson (ETH Zurich)
DTSTART:20201202T130000Z
DTEND:20201202T140000Z
DTSTAMP:20260423T041811Z
UID:QMULANTS/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QMULANTS/7/"
 >Theta functions\, fourth moments of eigenforms and the sup-norm problem</
 a>\nby Paul Nelson (ETH Zurich) as part of Queen Mary University of London
  Algebra and Number Theory Seminar\n\n\nAbstract\nI will discuss joint wor
 k with Raphael Steiner and Ilya Khayutin in which we study the sup norm pr
 oblem for GL(2) eigenforms in the squarefree level aspect.  Unlike the sta
 ndard approach to the problem via arithmetic amplification following Iwani
 ec--Sarnak\, we apply a method\, introduced earlier in other aspects by my
  collaborators\, which consists of identifying a fourth moment over a fami
 ly of eigenforms evaluated at the point of interest with the L^2-norm of a
  theta function defined using the correspondence of Eichler\, Shimizu and 
 Jacquet--Langlands.  After solving some counting problems (involving both 
 "linear" sums as in traditional approaches and new "bilinear" sums)\, we o
 btain a bound comparable to the fourth root of the volume\, improving upon
  the trivial square root bound and the nontrivial cube root bound establis
 hed by Harcos--Templier and Blomer--Michel.  I will describe the proof in 
 the simplest case.\n
LOCATION:https://researchseminars.org/talk/QMULANTS/7/
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