Beyond Endoscopy for the relative trace formula II: global 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.

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

References in corpus (3)

• A conjecture on Whittaker-Fourier coefficients of cusp forms
• The Schwartz space of a smooth semi-algebraic stack
• Beyond Endoscopy via the Trace Formula-I: Poisson Summation and Contributions of Special Representations

Cited by in corpus (2)

• Functorial transfer between relative trace formulas in rank one
• On the Fourier transform of regularized Bessel functions on complex numbers and Beyond Endoscopy over number fields