Critical p-adic L-functions

Critical slope p-adic L-functions

Let g be an eigenform of weight k+2 on Γ0(p)∩Γ1(N) with p N . If g is non-critical (i.e. of slope less than k + 1), using the methods of [1, 20], one can attach a p-adic L-function to g which is uniquely determined by its interpolation property together with a bound on its growth. However, in the critical slope case, the corresponding growth bound is too large to uniquely determine the p-adic L...

CRITICAL SLOPE p-ADIC L-FUNCTIONS – DRAFT

Let p be a prime number, and let f = ∑ n anq n denote a normalized cuspidal eigenform of weight k + 2 on Γ0(N) with p N . If f is a p-ordinary form, then by [1, 17] we can attach a p-adic L-function to f which interpolates special values of its L-series. On the other hand, if f is non-ordinary at p, we have two p-adic L-functions attached to f , one for each root of x − apx + p. These two roots...

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...