Identities of symmetry for generalized twisted Bernoulli polynomials twisted by unramified roots of unity

Details Identities of symmetry for generalized twisted Bernoulli polynomials twisted by unramified roots of unity Identities of symmetry for generalized twisted Bernoulli polynomials twisted by unramified roots of unity

2010-04-23

arxiv.org/abs/1004.4038v1

Mathematics

Number Theory

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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.

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