Beyond endoscopy for the relative trace formula II: Global theory

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For the group we perform a comparison between two relative trace formulas: On the one hand, the relative trace formula of Jacquet for the quotient , where is a nontrivial torus, and on the other the Kuznetsov trace formula (involving Whittaker periods), applied to nonstandard test functions. This gives a new proof of the celebrated result of Waldspurger on toric periods, and suggests a new way of comparing trace formulas, with some analogies to Langlands' 'Beyond Endoscopy' program.

Original languageEnglish (US)
Pages (from-to)347-447
Number of pages101
JournalJournal of the Institute of Mathematics of Jussieu
Issue number2
StatePublished - Mar 1 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • L-functions
  • Waldspurger's formula
  • beyond endoscopy
  • periods
  • relative trace formula

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