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.

Keywords

Linear periods / Relative trace formulae / Fundamental lemma / Smooth matching / 11F70

References

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Funding

Division of Mathematical Sciences(1901862)

RIGHTS & PERMISSIONS

Peking University