On gamma factors of generic representations of $\mathrm{U}_{2n+1}\times\operatorname{Res}_{E/F}\operatorname{GL}_{r}$

Yao Cheng and Chian-Jen Wang

Vol. 337 (2025), No. 1, 25–85

DOI: 10.2140/pjm.2025.337.25

Abstract

We develop fundamental properties of the Rankin–Selberg gamma factors for generic representations of ${U<!--FUNCTION\; APPLICATION-->}_{2n+1}\times {\mathrm{Res}<!--FUNCTION\; APPLICATION-->}_{E∕F}{\mathrm{GL}<!--FUNCTION\; APPLICATION-->}_r$ over local fields under a natural assumption on the Archimedean local integrals. In particular, the gamma factors defined by the Rankin–Selberg method are shown to coincide with those defined by the Langlands–Shahidi method.

Keywords

Rankin–Selberg integrals, gamma factors, unitary groups

Mathematical Subject Classification

Primary: 11F70

Secondary: 22E50

Milestones

Received: 28 March 2024

Revised: 10 March 2025

Accepted: 15 March 2025

Published: 2 June 2025