Second order average estimates on local data of cusp forms

2005/10/05 by Farrell Brumley, Brumley, Farrell · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0510089

openalex publication_date 2005/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We specify sufficient conditions for the square modulus of the local parameters of a family of GL(n) cusp forms to be bounded on average. These conditions are global in nature and are at present satisfied for n less than or equal to 4. As an application, we show that Rankin-Selberg L-functions on GL(m) x GL(n), when m and n are less than or equal to 4, satisfy the standard convexity bound.

Citations

• Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique

Cited by

• Large sieves for GL_n and applications
• On Hypothesis H of Rudnick and Sarnak

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