Strong multiplicity one for the Selberg class

2002/10/18 by K. Soundararajan, Kannan Soundararajan, Soundararajan, Kannan
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0210299

7 pages

arxiv created 2002/10/18 · openalex publication_date 2002/10/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we investigate the problem of determining elements of the Selberg class from their Dirichlet series coefficients at the primes. We show that this is possible when the degree is one, but in general need an additional weak hypothesis on the Dirichlet series coefficients at squares of primes.

Citations

• Hilbert's Inequality
• Zeros of principal L-functions and random matrix theory

Related

• Strong multiplicity one for the Selberg class
• Mertens' theorem and prime number theorem for Selberg class
• Beyond the extended Selberg class: 1
• The Selberg trace formula as a Dirichlet series
• Degree 1 elements of the Selberg class