We construct a Shintani lift for rigid analytic cocycles of higher weight, attaching modular forms of half-integral weight to such cocycles. The expression for the Fourier coefficients of the modular form RS(J) attached to a cocycle J is given in terms of the residues of J, and shares a striking similarity with the expression for the coefficients of the classical Shintani lift S(f) of an integral weight modular form f. This work aligns with the ideas of the nascent p-adic Kudla program and strengthens the analogy between rigid cocycles and modular forms.
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Isabella Negrini (2024) studied this question.
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