p-adic modular forms of non-integral weight over Shimura curves

p - adic Modular Forms over Shimura Curves over

In this thesis, we set up the basic theory of p-adic modular forms over Shimura curves over Q, parallel to the classical case over modular curves. We define and study the structure of the spaces of p-adic modular forms with respect to certain quaternion algebras over Q. We study the relation of these modular forms with classical quaternionic modular forms. We prove a canonical subgroup theorem ...

p-adic interpolation of half-integral weight modular forms

The p-adic interpolation of modular forms on congruence subgroups of SL2(Z) has been succesfully used in the past to interpolate values of L-series. In [12], Serre interpolated the values at negative integers of the ζ-series of a totally real number field (in fact of L-series of powers of the Teichmuller character) by interpolating Eisenstein series, which are holomorphic modular forms, and loo...

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

P -adic Family of Half-integral Weight Modular Forms via Overconvergent Shintani Lifting

The classical Shintani map (see [Shn]) is the Hecke-equivariant map from the space of cusp forms of integral weight to the space of cusp forms of half-integral weight. In this paper, we will construct a Hecke-equivariant overconvergent Shintani lifting which interpolates the classical Shintani lifting p-adically, following the idea of G. Stevens in [St1]. In consequence, we get a formal q-expan...

GEOMETRIC AND p-ADIC MODULAR FORMS OF HALF-INTEGRAL WEIGHT by