For zoom details contact Pieter Moree (moree@mpim-bonn.mpg.de).

The Guo-Jacquet conjecture is a promising generalisation to higher dimensions of Waldspurger’s well-known theorem relating toric periods to central values of automorphic L-functions for $GL(2)$. Some cases of this conjecture have been proved by Feigon-Martin-Whitehouse via the comparison of simple relative trace formulae. However, if we want to obtain more general results, we need to establish and compare more general relative trace formulae, where some analytic difficulties such as the divergence issue should be addressed. In my thesis supervised by Chaudouard, analogues of these problems were studied at the infinitesimal level. In particular, we have established an infinitesimal variant of Guo-Jacquet trace formulae and certain identities between Fourier transforms of local weighted orbital integrals. In this talk, we plan to talk about these results and explain some ingredients in the proof. Time permitting, we may also discuss an ongoing work on the application to the transfer of weighted orbital integrals.

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