2013/04/16 by Guglielmo Fucci, Klaus Kirsten
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #Analytic continuation #Arithmetic zeta function #Complex plane #Continuation #Function (biology) #Gamma function #L-function #Mathematical analysis #Mathematics #Meromorphic function #Polylogarithm #Prime zeta function #Pure mathematics #Riemann zeta function #math-ph #math.CV #math.MP
paper · pdf · doi:10.1016/j.amc.2013.06.092
published as Appl. Math. Comput. 221 (2013) 598 - 609 · 18 pages, Latex, 3 Figures
arxiv created 2013/04/16 · openalex publication_date 2013/07/30 · arxiv updated 2013/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The aim of this work is to study the analytic continuation of the doubly-periodic Barnes zeta function. By using a suitable complex integral representation as a starting point we find the meromorphic extension of the doubly periodic Barnes zeta function to the entire complex plane in terms of a real integral containing the Hurwitz zeta function and the first Jacobi theta function. These allow us to explicitly give expressions for the derivative at all non-positive integer points.