Subconvexity bounds for automorphic L-functions

A. Diaconu, P. Garrett

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We break the convexity bound in the t-aspect for L-functions attached to cusp forms f for GL2(k) over arbitrary number fields k. The argument uses asymptotics with error term with a power saving, for second integral moments over spectral families of twists L(s,f⊗X) by Grossencharacters , from our previous paper on integral moments.

Original languageEnglish (US)
Pages (from-to)95-124
Number of pages30
JournalJournal of the Institute of Mathematics of Jussieu
Issue number1
StatePublished - Jan 2010

Bibliographical note

Funding Information:
Acknowledgements. Both authors were partially supported by NSF Grant DMS-0652488. We would like to acknowledge useful comments and advice from P. Sarnak. We also thank the anonymous referee for helpful comments and suggestions.


  • Eisenstein series
  • Integral moments
  • L-functions
  • Meromorphic continuation
  • Poincaré series
  • Spectral decomposition
  • Subconvexity


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