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Article Dans Une Revue International Journal of Number Theory Année : 2023

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

Résumé

Koecher in 1980 derived a method for obtaining identities for the Riemann zeta function at odd positive integers, including a classical result for [Formula: see text] 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 [Formula: see text].

Dates et versions

hal-04407695 , version 1 (21-01-2024)

Identifiants

Citer

Karl Dilcher, Christophe Vignat. On a result of Koecher concerning Markov–Apéry-type formulas for the Riemann zeta function. International Journal of Number Theory, 2023, 19 (04), pp.709-731. ⟨10.1142/S1793042123500355⟩. ⟨hal-04407695⟩
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