A Note on p-adic Rankin–Selberg L-functions

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...

A note on some expansions of p - adic functions

Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by (φm)m∈N0 . The system (φm)m∈N0 is defined in the space C(Zp,Cp) of Cp-valued continuous functions on Zp. J. Rutkowski has also considered some questions concerning expansions of functions from C(Zp,Cp) with respect to (φm)m∈N0 . This paper is a remark to Rutkowski’s paper....

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

Eisenstein Cohomology and p - adic L - Functions

§0. Introduction. In this paper, we define the module D̃(V ) of distributions with rational poles on a finite dimensional rational vector space a V . This is an infinite dimensional vector space over Q endowed with a natural action of the reductive group GV := Aut(V ). Indeed, this action extends to a natural action of the adelic group GV (AQ). For each prime p, we define we define the notion of...

SUPERSINGULAR PRIMES AND p-ADIC L-FUNCTIONS

We discuss the problem of finding a p-adic L-function attached to an elliptic curve with complex multiplication over an imaginary quadratic field K, for the case of a prime where the curve has supersingular reduction. While the case of primes of ordinary reduction has been extensively studied and is essentially understood, yielding many deep and interesting results, basic questions remain unans...