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SUMMARY:Distribution of Hecke eigenvalues - Jasmin Matz (University of Cop
 enhagen)
DTSTART:20200128T143000Z
DTEND:20200128T153000Z
UID:TALK135295@talks.cam.ac.uk
CONTACT:Jessica Fintzen
DESCRIPTION:There are many difficult conjectures about automorphic\nrepres
 entations\, many of which seem to be out of reach at the moment.\nIt has t
 herefore become increasingly popular to study instead families\nof automor
 phic representations and their statistical properties\, which\nallows for 
 additional analytic techniques to be used.\n\nIn my talk I want to discuss
  the distribution of Hecke eigenvalues\nor\, in other words\, Satake param
 eters in the family of spherical\nunramified automorphic representations o
 f split classical groups.  We\nobtain an effective distribution of the Sat
 ake parameters\, when we\norder the family according to the size of analyt
 ic conductor. This has\napplications to various 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 symmetr
 ic space. This\nis joint work with T. Finis.
LOCATION:MR13
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