Automorphic spectral identities and applications to automorphic L-functions on GL2

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We prove an automorphic spectral identity on GL2 involving second moments. From it we obtain an asymptotic, with powersaving error term, for (non-archimedean) conductor-aspect integral moments, twisting by GL1 characters ramifying at a fixed finite place. The strength of the spectral identity, and of the resulting asymptotics, is illustrated by extracting a subconvex bound in conductor aspect at a fixed finite prime.

Original languageEnglish (US)
Pages (from-to)278-317
Number of pages40
JournalJournal of Number Theory
Issue number1
StatePublished - 2013

Bibliographical note

Funding Information:
This research was partially supported by NSF grant DMS-0652488. E-mail address:

Publisher Copyright:
© 2012 Elsevier Inc. All rights reserved.

Copyright 2018 Elsevier B.V., All rights reserved.


  • Automorphic L-functions
  • Conductor aspect
  • Integral moments
  • Poincaré series
  • Spectral decomposition
  • Subconvexity


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