p-adic families of d-th Shintani liftings

Daniele Casazza; Carlos de Vera-Piquero

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arXiv · 1912.05655

p-adic families of d-th Shintani liftings

Daniele Casazza·Carlos de Vera-Piquero

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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.

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Daniele Casazza, Carlos de Vera-Piquero. 2019-12-11. p-adic families of d-th Shintani liftings. https://arxiv.org/abs/1912.05655

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