Arithmetic theory of harmonic numbers
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Publication:3116531
DOI10.1090/S0002-9939-2011-10925-0zbMath1271.11021OpenAlexW1980788403MaRDI QIDQ3116531
Publication date: 24 February 2012
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9939-2011-10925-0
Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Bernoulli and Euler numbers and polynomials (11B68) Other combinatorial number theory (11B75) Congruences; primitive roots; residue systems (11A07)
Related Items (26)
PROOF OF A CONGRUENCE FOR HARMONIC NUMBERS CONJECTURED BY Z.-W. SUN ⋮ Congruences involving \(g_n(x)=\sum\limits_{k=0}^n\dbinom{n}{k}^2\dbinom{2k}{k}x^k\) ⋮ On functional equations of finite multiple polylogarithms ⋮ Proof of a Dwork-type supercongruence by induction ⋮ Unnamed Item ⋮ Congruences for Franel numbers ⋮ Four families of summation formulas involving generalized harmonic numbers ⋮ Summation formulas involving generalized harmonic numbers ⋮ On two congruences involving Franel numbers ⋮ An extension of a congruence by Tauraso ⋮ Modulo $p^2$ congruences involving harmonic numbers ⋮ On some conjectural hypergeometric congruences ⋮ Supercongruences motivated by \(e\) ⋮ A Saalschütz-type identity and summation formulae involving generalized harmonic numbers ⋮ Finite and étale polylogarithms ⋮ Some congruences on harmonic numbers and binomial sums ⋮ Some congruences with $q-$binomial coefficients and $q-$harmonic numbers ⋮ Whipple-type 3F2-series and summation formulae involving generalized harmonic numbers ⋮ Two congruences involving harmonic numbers with applications ⋮ Watson-type3F2-series and summation formulae involving generalized harmonic numbers ⋮ Modulo \(p^2\) congruences involving generalized harmonic numbers ⋮ ON CONGRUENCES WITH THE TERMS OF THE SECOND ORDER SEQUENCES fUkng AND fVkng ⋮ Efficient approximations of finite and infinite real alternating p -series ⋮ Two congruences concerning Apéry numbers conjectured by Z.-W. Sun ⋮ Some congruences related to the q-Fermat quotients ⋮ On the congruence of finite sums involving generalized harmonic numbers modulo $p^2$
Cites Work
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- New identities involving Bernoulli and Euler polynomials
- Symmetric identities on Bernoulli polynomials
- New congruences for central binomial coefficients
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- Identities concerning Bernoulli and Euler polynomials
- A Generalization of Wolstenholme's Theorem
- A Stirling Encounter with Harmonic Numbers
- On an Intriguing Integral and Some Series Related to ζ(4)
- Variations on Wolstenholme's Theorem
- WOLSTENHOLME TYPE THEOREM FOR MULTIPLE HARMONIC SUMS
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