Jeehoon Park
p-adic family of half-integral weight modular forms via overconvergent 
Shintani Lifting

Abstract:
The classical Shintani map 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
talk, I will describe a Hecke-equivariant overconvergent
Shintani lifting which interpolates the classical Shintani lifting
$p$-adically (part 1). In consequence, we get a formal $q$-expansion 
$\Theta$ whose
$q$-coefficients are in an overconvergent distribution ring, which
can be thought of $p$-adic analytic family of overconvergent
modular forms of half-integral weight, since the specializations
of $\Theta$ at the arithmetic weights are the classical cusp forms
of half-integral weight (part 2).