English

Beyond Endoscopy for the relative trace formula II: global theory

Number Theory 2019-02-27 v3 Representation Theory

Abstract

For the group G=PGL_2 we perform a comparison between two relative trace formulas: on one hand, the relative trace formula of Jacquet for the quotient T\backslash G/T, where T is a non-trivial torus, and on the other the Kuznetsov trace formula (involving Whittaker periods), applied to non-standard 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.

Keywords

Cite

@article{arxiv.1402.3524,
  title  = {Beyond Endoscopy for the relative trace formula II: global theory},
  author = {Yiannis Sakellaridis},
  journal= {arXiv preprint arXiv:1402.3524},
  year   = {2019}
}

Comments

109pp, improved presentation at various points, to appear in J. Inst. Math. Jussieu

R2 v1 2026-06-22T03:08:32.586Z