An infinitesimal variant of Guo-Jacquet trace formulae and its comparison

Abstract: The Guo-Jacquet conjecture is a promising generalization to higher dimensions of Waldspurger’s well-known theorem relating toric periods to central values of automorphic L-functions for $GL(2)$. Feigon-Martin-Whitehouse have proved some cases of this conjecture using simple relative trace formulae, Guo’s work on the fundamental lemma and C. Zhang’s work on the transfer. However, if we want to obtain more general results, we have to establish and compare more general relative trace formulae, where some analytic difficulties such as the divergence issue should be addressed.

In this talk, we plan to study analogues of these problems at the infinitesimal level. After briefly introducing the background, we shall present an infinitesimal variant of Guo-Jacquet trace formulae. To compare regular semi-simple terms in these formulae, we shall discuss the weighted fundamental lemma and certain identities between Fourier transforms of local weighted orbital integrals. During the proof, we also need some results in local harmonic analysis such as local trace formulae for some $p$-adic infinitesimal symmetric spaces. This talk is based on my thesis supervised by P.-H. Chaudouard.

algebraic geometrynumber theory

Audience: researchers in the topic

( slides )

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MIT number theory seminar

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