Multiple p-adic L-function

Multivariate P-adic L-function

In the recent, many mathematicians studied the multiple zeta function in the complex number field. In this paper we construct the p-adic analogue of multiple zeta function which interpolates the generalized multiple Bernoulli numbers attached to χ at negative integers. §1. Introduction Let p be a fixed prime. Throughout this paper Z p , Q p , C and C p will, respectively, denote the ring of p-a...

The “missing” p-adic L-function – DRAFT

JACOBI FORMS AND A TWO-VARIABLE p-ADIC L-FUNCTION

Introduction. Consider a Jacobi form φ(τ, z) = ∑ n,r c(n, r)q ζ whose Fourier coefficients c(n, r) are algebraic numbers. Let p be an odd prime. In this paper we associate to φ a Λ-adic p-ordinary form in the sense of [4]. The construction comes from the map Dν introduced in [2], Theorem 3.1. This map associates to a Jacobi form a family of modular forms parametrised by ν. We obtain the two-var...

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES

Further Remarks on Multiple p-adic q-L-Function of Two Variables

Abstract : The object of this paper is to give several properties and applications of the multiple p-adic q-L-function of two variables L (r) p,q (s, z, χ). The explicit formulas relating higher order qBernoulli polynomials, which involve sums of products of higher order q-zeta function and higher order Dirichlet q-L-function are given. The value of higher order Dirichlet p-adic q-L-function fo...