An explicit expression of the Lerch zeta function on maximal domains of holomorphy

2022/06/18 by Kozuma, Rintaro
#Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2206.09234

Abstract

We give two results on the Lerch zeta function Φ(z, s, w). The first is to give an explicit expression providing both the analytic continuation of Φ in n-variables (n ∈ \1, 2, 3\) to maximal domains of holomorphy in ℂⁿ with computable evaluation and an extended formula for the special values of Φ at non-positive integers in the variable s. The second is to show that Lerch's functional equation is essentially the same as Apostol's functional equation using the first result.

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