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

TL;DR

This paper introduces eight new identities of symmetry involving three variables for generalized twisted Bernoulli polynomials and power sums, expanding previous work limited to two-variable identities, using p-adic integral techniques.

Contribution

It presents novel three-variable symmetry identities for generalized twisted Bernoulli polynomials and power sums, derived via p-adic integral methods, extending prior two-variable results.

Findings

Eight new identities of symmetry in three variables.

Use of p-adic integrals to derive identities.

Extension from two-variable to three-variable symmetry identities.

Abstract

We derive eight identities of symmetry in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by ramified roots of unity. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the $p$-adic integral expression 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.