New series for some special values of $L$-functions

zbMath1349.11127arXiv1010.4298MaRDI QIDQ2990672

Zhi-Wei Sun

Publication date: 10 August 2016

Full work available at URL: https://arxiv.org/abs/1010.4298

zbMATH Keywords

congruenceseriesharmonic numberRiemann's zeta functioncentral binomial coefficientDirichlet's \(L\)-function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Congruences; primitive roots; residue systems (11A07)

Related Items (13)

Supercongruences involving dual sequences ⋮ Another look at Zagier's formula for multiple zeta values involving Hoffman elements ⋮ On two conjectures of Sun concerning Apéry-like series ⋮ Infinite series about harmonic numbers inspired by Ramanujan-like formulae ⋮ New series for powers of \(\pi\) and related congruences ⋮ Alternating multiple zeta values, and explicit formulas of some Euler-Apéry-type series ⋮ Proof of some conjectural hypergeometric supercongruences via curious identities ⋮ Further Apéry-like series for Riemann zeta function ⋮ New series involving harmonic numbers and squared central binomial coefficients ⋮ Explicit formulas of sums involving harmonic numbers and Stirling numbers ⋮ Alternating series of Apéry-type for the Riemann zeta function. ⋮ Infinite Summation Formulas Involving Riemann-Zeta function ⋮ Congruences for certain families of Apéry-like sequences

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