A genus two arithmetic Siegel-Weil formula on 𝑋₀(𝑁)

Abstract

We define a family of arithmetic zero cycles in the arithmetic Chow group of a modular curve X 0 ( N ) X_0(N) , for N > 3 N>3 odd and squarefree, and identify the arithmetic degrees of these cycles as q q -coefficients of the central derivative of a Siegel Eisenstein series of genus two. This parallels work of Kudla-Rapoport-Yang for Shimura curves.