\(p\)-adic family of half-integral weight modular forms via overconvergent Shintani lifting (Q2268168)

The author proves that there exists a formal \(q\)-expansion \(\Theta\) with coefficients in an overconvergent distribution ring whose specializations to classical arithmetic points are, up to multiplication by scalars, the \(q\)-expansions of Hecke eigenforms of half-integral weight. This is obtained via Shintani's map from the cuspidal Hecke eigenforms of tame level with finite slope.