Critical slope 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...

Iwasawa theory of overconvergent modular forms, I: Critical-slope p-adic L-functions

We construct an Euler system of p-adic zeta elements over the eigencurve which interpolates Kato’s zeta elements over all classical points. Applying a big regulator map gives rise to a purely algebraic construction of a two-variable p-adic L-function over the eigencurve. As a first application of these ideas, we prove the equality of the p-adic L-functions associated with a critical-slope refin...

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...