  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 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 Lamda-adic lifting of this map to the Hida family of ordinary cusp
forms of integral weight and consequently constructed Lamda-adic modular eigen
form of half-integral weight. The natural thing to do is generalizing his
result to non-ordinary finite slope case, i.e. Coleman p-adic analytic family
of overconvergent cusp forms of finite slope. For this we will use a slope h
decomposition of compact supported cohomology with values in overconvergent
distribution, which can be interpreted as a cohomological description of
Coleman p-adic family, and define the p-adic Hecke algebra for the slope h part
of this cohomology. Then we follow the idea of [St1] in the ordinary case. We
also describe Hecke operators explicitly on q-expansion of universal
overconvergent half-integral weight modular forms using the Hecke actions on
overconvergent modular symbol.
