Hida families and p-adic triple product L-functions

Several Variables p-Adic L-Functions for Hida Families of Hilbert Modular Forms

After formulating Conjecture A for p-adic L-functions defined over ordinary Hilbert modular Hida deformations on a totally real field F of degree d, we construct two p-adic L-functions of d+1-variable depending on the parity of weight as a partial result on Conjecture A. We will also state Conjecture B which is a corollary of Conjecture A but is important by itself. Main issues of the construct...

p-adic measures and square roots of special values of triple product L-functions

Introduction Let p be a prime number. In this note, we combine the methods of Hida with the results of [HK1] to define a p-adic analytic function, the squares of whose special values are related to the values of triple product L-functions at their centers of symmetry. More precisely, let f , g, and h be classical normalized cuspidal Hecke eigenforms of level 1 and (even) weights k, l, and m, re...

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

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...