Periods and global invariants of automorphic representations

Joseph Bernstein, Andre Reznikov

Research output: Contribution to journalArticlepeer-review


We consider periods of automorphic representations of adele groups defined by integrals along Gelfand subgroups. We define natural maps between local components of such periods and construct corresponding global maps using automorphic L-functions. This leads to an introduction of a global invariant of an automorphic representation arising from two such periods. We compute this invariant in some cases.

Original languageEnglish
Pages (from-to)117-159
Number of pages43
JournalJournal of Number Theory
StatePublished - Feb 2023

Bibliographical note

Funding Information:
The research was partially supported by the ERC FP7 grant 291612 , by the ISF grant 533/14 , and, during the visit to IAS, by the National Science Foundation under Grant No. DMS - 1638352 .

Publisher Copyright:
© 2022 Elsevier Inc.


  • Automorphic representations
  • Co-invariants
  • L-functions
  • Periods


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