Twisted arithmetic Siegel Weil formula on X0(N)

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 equivalent to r(2) mod 4N and Delta is a fundamental discriminant, we construct a twisted arithmetic theta function (phi) over cap (Delta,r)(tau) which is a generating function of arithmetic twisted Heegner divisors. We prove that the arithmetic pairing <(phi) over cap (Delta,r)(tau),(omega) over cap (N)> is equal to the special value, rather than the derivative, of some Eisenstein series, thanks to some cancellation, where (omega) over cap (N) is a normalized metric Hodge line bundle. We also prove the modularity of (phi) over cap (Delta,r)(tau). (C) 2019 Elsevier Inc. All rights reserved.