The multiple Dirichlet product and the multiple Dirichlet series

2016/01/22 by Tomokazu Onozuka, Onozuka, Tomokazu
Mathematics · #11A25 #11M32 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Functional Equations Stability Results #Number Theory (math.NT) #math.NT #msc:11A25 #msc:11M32

paper · pdf · doi:10.48550/arxiv.1601.05924

15 pages

arxiv created 2016/01/22 · openalex publication_date 2016/01/22 · arxiv updated 2016/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

First, we define the multiple Dirichlet product and study the properties of it. From those properties, we obtain a zero-free region of a multiple Dirichlet series and a multiple Dirichlet series expression of the reciprocal of a multiple Dirichlet series.

Related

• Multiple Dirichlet series associated to additive and Dirichlet characters
• A survey on the theory of multiple Dirichlet series with arithmetical coefficients on the numerators
• On the parity result for multiple Dirichlet series
• General multiple Dirichlet series from perverse sheaves
• Discrete restrictions from Laurent monomial systems for multiple Dirichlet series