A Note on Twisted Bernoulli Measures

Abstract

We introduce the twisted Bernoulli measures as a family of p-adic measures parametrized by the complement of the open disc with radius 1 and centered at 1 in the completion of an algebraic closure of p-adic numbers. These measures are the higher order versions of the measure used by Koblitz and Coleman to interpret (p-adic) polylogarithms. We also prove that these measures are the unique p-adic measures that can be obtained from polynomials over the field Q(y) which is similar to the uniqueness property of Bernoulli measures.