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arXiv · 2509.18062

Introduction to the relative Langlands program

Raphaël Beuzart-Plessis
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Abstract

The aim of these notes is to give an overview of several aspects of what has come to be called the relative Langlands program, a theme that takes its origin in the study of automorphic periods and their relations to particular cases of Langlands functoriality and special values of (automorphic) $L$-functions. Following the work of Sakellaridis and Sakellaridis-Venkatesh, we emphasize the unifying role played by spherical varieties and harmonic analysis on them. We also review various instances of the phenomena, discovered by Jacquet, Gan-Gross-Prasad, Ichino-Ikeda and many others, that motivated these developments.

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Raphaël Beuzart-Plessis. 2025-09-22. Introduction to the relative Langlands program. https://arxiv.org/abs/2509.18062

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