Twisted arithmetic Siegel Weil formula on X0(N)
arXiv:1801.01819
Abstract
In this paper, we study twisted arithmetic divisors on the modular curve X_0(N) with N square-free. For each pair (Î, r) where Î>0 and Î\equiv r^2 \mod 4N, we constructed a twisted arithmetic theta function Ï_{Î, r}(Ï) which is a generating function of arithmetic twisted Heegner divisors. We prove the modularity of Ï_{Î, r}(Ï), along the way, we also identify the arithmetic pairing \langle Ï_{Î, r}(Ï),\widehatÏ_N \rangle with special value of some Eisenstein series, where \widehatÏ_N is a normalized metric Hodge line bundle.
27pages