The Twisted Doubling Method in Algebraic Families

2024/10/29 by Johannes Girsch, Girsch, Johannes · 1 citation
Computer Science · Engineering · #11F70 11S40 22E50 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2410.22525

openalex publication_date 2024/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the twisted doubling zeta integrals of Cai-Friedberg-Ginzburg-Kaplan in the setting of algebraic families. We then prove a rationality result and a functional equation for these zeta integrals. This allows us to define an unnormalized γ-factor associated to certain families of representation of a classical group times a general linear group.

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• The universal Harish-Chandra j-function

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