P-adic L-functions in universal deformation families

p-ADIC L-FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS

We construct the p-adic standard L-functions for ordinary families of Hecke eigensystems of the symplectic group Sp(2n)/Q using the doubling method. We explain a clear and simple strategy of choosing the local sections for the Siegel Eisenstein series on the doubling group Sp(4n)/Q, which guarantees the nonvanishing of local zeta integrals and allows us to p-adically interpolate the restriction...

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...

L-FUNCTIONS OF p-ADIC CHARACTERS

We define a p-adic character to be a continuous homomorphism from 1 + tFq [[t]] to Zp. For p > 2, we use the ring of big Witt vectors over Fq to exhibit a bijection between p-adic characters and sequences (ci)(i,p)=1 of elements in Zq , indexed by natural numbers relatively prime to p, and for which limi→∞ ci = 0. To such a p-adic character we associate an L-function, and we prove that this L-f...