SOME SYMMETRY IDENTITIES FOR GENERALIZED TWISTED BERNOULLI POLYNOMIALS TWISTED BY UNRAMIFIED ROOTS OF UNITY

DOI10.4134/BKMS.2015.52.2.603zbMATH Open1393.11020arXiv1004.4038OpenAlexW2030578266MaRDI QIDQ5246041

Dae San Kim

Publication date: 17 April 2015

Published in: Bulletin of the Korean Mathematical Society (Search for Journal in Brave)

Abstract: We derive three identities of symmetry in two variables and eight in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by unramified roots of unity. The case of ramified roots of unity was treated previously. The derivations of identities are based on the $p$-adic integral expression, with respect to a measure introduced by Koblitz, of the generating function for the generalized twisted Bernoulli polynomials and the quotient of $p$-adic integrals that can be expressed as the exponential generating function for the generalized twisted power sums.

Full work available at URL: https://arxiv.org/abs/1004.4038

zbMATH Keywords

Dirichlet character\(p\)-adic integralidentities of symmetrygeneralized twisted Bernoulli polynomialgeneralized twisted power sumunramified roots of unity

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80)

Related Items (1)

On the symmetric properties for the generalized twisted Bernoulli polynomials

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