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arXiv · 2112.11379

The Shimura-Shintani correspondence via singular theta lifts and currents

Jonathan Crawford·Jens Funke
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Abstract

We describe the construction and properties of a singular theta lift for the orthogonal group $\SO(2,1)$. We obtain locally harmonic Maass forms in the sense of Bringmann-Kane-Kohnen with singular sets along geodesics in the upper half plane. We consider these forms as currents and derive properties of the Shimura-Shintani correspondence. This work provides extensions of the theta lifts considered by Hoevel and Bringann-Kane-Viazovska.

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Jonathan Crawford, Jens Funke. 2021-12-21. The Shimura-Shintani correspondence via singular theta lifts and currents. https://arxiv.org/abs/2112.11379

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