PRODUCT OF RANKIN-SELBERG CONVOLUTIONS AND A NEW PROOF OF JACQUET’S LOCAL CONVERSE CONJECTURE
Abstract
Abstract This article constructs a family of integrals representing the product of Rankin–Selberg L -functions for GL l × GL m ${\mathrm {GL}}_l \times {\mathrm {GL}}_m$ upper G upper L Subscript l Baseline times upper G upper L Subscript m and GL l × GL n ${\mathrm {GL}}_l \times {\mathrm {GL}}_n$ upper G upper L Subscript l Baseline times upper G upper L Subscript n in the regime m + n < l $m+n m plus n less than l . When n = 0 $n=0$ n equals 0 , these integrals reduce (up to a shift) to the classical Rankin-Selberg convolution integrals of Jacquet–Piatetski-Shapiro–Shalika (JPSS), thereby generalizing the JPSS integrals. We establish their basic properties and use them to define local gamma factors. As an application, we provide a new proof of Jacquet’s local converse conjecture.
Fields of Study & Subjects
Advanced Algebra and Geometry
Analytic Number Theory Research
Advanced Mathematical Identities
Publication details
- Journal / source
- Journal of the Institute of Mathematics of Jussieu
- Publisher
- Cambridge University Press (CUP)
- Volume
- 25
- Issue
- 6
- Pages
- 1–75
- Publication date
- 10 August 2026
- Language
- EN