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CATEGORIES:Number Theory Seminar
SUMMARY:Distribution of Hecke eigenvalues - Jasmin Matz (U
 niversity of Copenhagen)
DTSTART;TZID=Europe/London:20200128T143000
DTEND;TZID=Europe/London:20200128T153000
UID:TALK135295AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/135295
DESCRIPTION:There are many difficult conjectures about automor
 phic\nrepresentations\, many of which seem to be o
 ut of reach at the moment.\nIt has therefore becom
 e increasingly popular to study instead families\n
 of automorphic representations and their statistic
 al properties\, which\nallows for additional analy
 tic techniques to be used.\n\nIn my talk I want to
  discuss the distribution of Hecke eigenvalues\nor
 \, in other words\, Satake parameters in the famil
 y of spherical\nunramified automorphic representat
 ions of split classical groups.  We\nobtain an eff
 ective distribution of the Satake parameters\, whe
 n we\norder the family according to the size of an
 alytic conductor. This has\napplications to variou
 s questions in number theory\, for example\,\nlow-
 lying zeros in families of automorphic L-functions
 \, but also yields\nan effective Weyl law for the 
 underlying locally symmetric space. This\nis joint
  work with T. Finis.
LOCATION:MR13
CONTACT:Jessica Fintzen
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