p-adic families of d-th Shintani liftings

Abstract

In this note we give a detailed construction of a $\Lambda$-adic $\mathfrak{d}$-th Shintani lifting. We derive a $\Lambda$-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 $\Lambda$-adic $\d$-th Shintani liftings and Stark--Heegner points.