A note on Dirichlet-like series attached to polynomials

2025/03/24 by Frédéric Chapoton, Chapoton, Frédéric
Mathematics · #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2503.18448

openalex publication_date 2025/03/24 · openalex created_date 2025/10/07 · openalex updated_date 2026/07/28

Abstract

Some Dirichlet-like functions, attached to a pair (periodic function, polynomial) are introduced and studied. These functions generalize the standard Dirichlet L-functions of Dirichlet characters. They have similar properties, being holomorphic on thefull complex plane and having simple values on negative integers.

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