On the Shintani lifting of integral weight modular forms to half-integral weight modular forms

Abstract

In this paper, we explore the adelic Shintani lifting of a weight 2 cusp form [Formula: see text]. For a finite Schwartz function related to an auxiliary quadratic character [Formula: see text], we express certain Fourier coefficients of this lifting in terms of the twisted [Formula: see text]-value [Formula: see text].