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A note on gamma factors for pairs

Omer Offen

Abstract

In this short note we observe that the gamma factor defined by Gelfand and Kazhdan coincides with the Rankin-Selberg root number defined by Jacquet, Piatetskii-Shapiro and Shalika.

A note on gamma factors for pairs

Abstract

In this short note we observe that the gamma factor defined by Gelfand and Kazhdan coincides with the Rankin-Selberg root number defined by Jacquet, Piatetskii-Shapiro and Shalika.

Paper Structure

This paper contains 5 sections, 1 theorem, 23 equations.

Table of Contents

  1. introduction
  2. Notation
  3. The Jacquet, Piateskii-Shapiro and Shalika construction
  4. The Gelfand-Kazhdan construction
  5. The comparison

Key Result

Theorem 5.1

Let $\pi$ be an irreducible cuspidal representation of $\operatorname{GL}_n(F)$ and $\tau$ an irreducible, generic representation of $\operatorname{GL}_{n-1}(F)$. Then

Theorems & Definitions (3)

  • Remark 1.1
  • Theorem 5.1
  • proof