On a result of Koecher concerning Markov-Apéry type formulas for the Riemann zeta function

2020/10/29 by Karl Dilcher, Dilcher, Karl, Christophe Vignat +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2010.15424

openalex publication_date 2020/10/29 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Koecher in 1980 derived a method for obtaining identities for the Riemann zeta function at odd positive integers, including a classical result for ζ(3) due to Markov and rediscovered by Apéry. In this paper we extend Koecher's method to a very general setting and prove two more specific but still rather general results. As applications we obtain infinite classes of identities for alternating Euler sums, further Markov-Apéry type identities, and identities for even powers of π

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