Asymptotic behavior of the Hurwitz-Lerch multiple zeta function at non-positive integer points

2021/11/11 by Hideki Murahara, Tomokazu Onozuka, Murahara, Hideki +1 · 2 citations
Mathematics · #11M32 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2111.06072

openalex publication_date 2021/11/11 · openalex created_date 2021/11/22 · openalex updated_date 2026/07/28

Abstract

We give a result on the asymptotic behavior of the Hurwitz-Lerch multiple zeta functions near non-positive integer points by using the Apostol-Bernoulli polynomials. From this result, we can evaluate limit values at non-positive integer points.

Cited by

• Stirling polynomials and multiple zeta (star) functions at non-positive integers
• Values at non-positive integers of partially twisted multiple zeta-functions II

Related

• Special values of generalized multiple Hurwitz zeta function at non-positive integers
• Instant Multiple Zeta Values at Non-Positive Integers and Bernoulli Functions
• Asymptotic coefficients of multiple zeta functions at the origin and generalized Gregory coefficients
• Analytic continuation of multiple zeta-functions and the asymptotic behavior at non-positive integers
• Zeta functions interpolating the convolution of the Bernoulli polynomials