  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.

Number Theory