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arXiv · 1801.01819

Twisted arithmetic Siegel Weil formula on X0(N)

Tuoping Du·Tonghai Yang
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Abstract

In this paper, we study twisted arithmetic divisors on the modular curve X_0(N) with N square-free. For each pair (\Delta, r) where \Delta >0 and \Delta \equiv r^2 \mod 4N, we constructed a twisted arithmetic theta function \phi_{\Delta, r}(\tau) which is a generating function of arithmetic twisted Heegner divisors. We prove the modularity of \phi_{\Delta, r}(\tau), along the way, we also identify the arithmetic pairing \langle \phi_{\Delta, r}(\tau),\widehat{\omega}_N \rangle with special value of some Eisenstein series, where \widehat{\omega}_N is a normalized metric Hodge line bundle.

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Tuoping Du, Tonghai Yang. 2018-01-05. Twisted arithmetic Siegel Weil formula on X0(N). https://arxiv.org/abs/1801.01819

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