Some symmetry identities for generalized twisted Bernoulli polynomials twisted by unramified roots of unity
Bull. Korean Math. Soc. 2015 Vol. 52, No. 2, 603-618
https://doi.org/10.4134/BKMS.2015.52.2.603
Published online March 31, 2015
Dae San Kim
Sogang University
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.
Keywords : generalized twisted Bernoulli polynomial, generalized twisted power sum, Dirichlet character, unramified roots of unity, $p$-adic integral, identities of symmetry
MSC numbers : 11B68, 11S80, 05A19
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