On Two Variable $p$-Adic $L$-Functions and a $p$-Adic Class Number Formula

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

Anticyclotomic p-adic L-functions and Ichino’s formula

We give a new construction of a p-adic L-function L(f,Ξ), for f a holomorphic newform and Ξ an anticyclotomic family of Hecke characters of Q( √ −d). The construction uses Ichino’s triple product formula to express the central values of L(f, ξ, s) in terms of Petersson inner products, and then uses results of Hida to interpolate them. The resulting construction is well-suited for studying what ...

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...

ON p-ADIC WALDSPURGER FORMULA

conjugation, c, 5anti-cyclotomic p-adic L-function, L (π), 6Atkin–Serre operator, Θord, 13 canonical pairing, ( ,)A, 23convergent modular form, M(m,K), 14admissible, 15of finite tame level, M[ (m,K), 14stable, M[ (m,K)♥, 14universal, 15 distribution algebraA-related, D(A,K), 25ω-related, D(ω,K), 25π-related, D(π), 4 global Lubin–Tate different...

On p-adic Artin L-functions II

Let p be a prime. Iwasawa’s famous conjecture relating Kubota-Leopoldt p-adic L-functions to the structure of certain Galois groups has been proven by Mazur and Wiles in [10]. Wiles later proved a far-reaching generalization involving p-adic L-functions for Hecke characters of finite order for a totally real number field in [14]. As we discussed in [5], an analogue of Iwasawa’s conjecture for p...