The p-adic Shintani cocycle

p-adic Deformation of Shintani Cycles

The goal of this thesis is to generalize to elliptic curves a classical formula of Hecke. This is chiefly achieved through studying p-adic deformation of certain Shintani cycles attached to a real quadratic field K and an elliptic curve E/Q of conductor N . Assume that all the prime divisors of N are split in K. Also suppose that E has multiplicative reduction at a prime p, and denote by f E th...

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...

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

Abstract. The goal of this paper is to construct the p-adic analytic family of overconvergent half-integral weight modular forms using Hecke-equivariant 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. Glenn Stevens proved in [St1] that there is ...

p-adic Shearlets

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.

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