A few remarks on values of Hurwitz Zeta function at natural and rational arguments

2014/05/24 by Paweł J. Szabłowski, Szabłowski, Paweł J.
Mathematics · #11J72 #11M06 #Advanced Mathematical Identities #FOS: Mathematics #Functional Equations Stability Results #Mathematical functions and polynomials #Number Theory (math.NT) #Primary 11M35 #Secondary 11M36

paper · pdf · doi:10.48550/arxiv.1405.6270

openalex publication_date 2014/05/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We exploit some properties of the Hurwitz zeta function ζ(n,x) in order to study sums of the form \frac1πⁿ∑_j=-∞^∞1/(jk+l)ⁿ and \frac1πⁿ∑_j=-∞^∞(-1)^j/(jk+l)ⁿ for % 2≤ n,k∈ ℕ, and integer l≤ k/2. We show that these sums are algebraic numbers. We also show that 1

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