On a Weighted Series of the Hurwitz Zeta Function

2023/02/03 by Fox, Matthew, Karamchedu, Chaitanya
#11M35 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2302.01865

Abstract

In this note we prove that for all a ∈ ℕ, x ∈ ℝ₊ ∪ \0\, and s ∈ ℂ with \Re(s) > a + 2, the (alternating) weighted series of the Hurwitz zeta function, ∑_{k ≥ 1} (± 1)^k (k + x)^aζ(s,k + x), resolves into a finite combination of Hurwitz (Lerch) zeta functions. This applies in Marichal and Zenaïdi's theory on analogues of the Bohr-Mollerup theorem for higher-order convex functions.

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