The Shimura-Shintani correspondence via singular theta lifts and currents
Abstract
We describe the construction and properties of a singular theta lift for the orthogonal group (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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