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