Twisted Linear Periods and a New Relative Trace Formula

Abstract

We study the linear periods on ${{\,\textrm{GL}\,}}_{2n}$ twisted by a character using a new relative trace formula. We establish the relative fundamental lemma and the transfer of orbital integrals. Together with the spectral isolation technique of Beuzart-Plessis–Liu–Zhang–Zhu, we are able to compare the elliptic part of the relative trace formulae and to obtain new results generalizing Waldspurger’s theorem in the $n=1$ case.

Funding

Division of Mathematical Sciences(1901642)