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Arithmetic Siegel-Weil formula on $X_{0}(N)$

Published 25 Feb 2017 in math.NT | (1702.07917v2)

Abstract: In this paper, we proved an arithmetic Siegel-Weil formula and the modularity of some arithmetic theta function on the modular curve $X_0(N)$ when $N$ is square free. In the process, we also construct some generalized Delta function for $\Gamma_0(N)$ and proved some explicit Kronecker limit formula for Eisenstein series on $X_0(N)$.

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