p-adic families of dth Shintani liftings

In this note we give a detailed construction of a Λ -adic d th Shintani lifting. We obtain a Λ -adic version of Kohnen’s formula relating Fourier coefficients of half-integral weight modular forms and special values of twisted L -series. As a by-product, we derive a mild generalization of such classical formulae, and also point out a relation between Fourier coefficients of Λ -adic d th Shintani liftings and Stark–Heegner points.