Riemann's Zeta Function: The alternating Xi-Function Xia(s)

2016/10/14 by Renaat Van Malderen, Van Malderen, Renaat · 1 citation
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1610.04344

openalex publication_date 2016/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

As well known, the study of Riemanns zeta function ζ(s) involves the related entire function ξ(s). A close relative of ζ(s) is the alternating zeta function η(s). Similar to ζ(s), also η(s) has a corresponding entire function ξ_a (s). After establishing its definition and a related functional equation, formulas based on incomplete gamma functions are worked out, allowing to numerically evaluate ξ_a (s). Examples verifying the obtained formulas are included.

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