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arXiv · 2502.19600

Intersections of Hecke correspondences on modular curves

Qiao He·Baiqing Zhu
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Abstract

We compute the arithmetic intersections of Hecke correspondences on the product of integral model of modular curve $\mathcal{X}_0(N)$ and relate it to the derivatives of certain Siegel Eisenstein series when $N$ is odd and squarefree. We prove this by establishing a precise identity between the arithmetic intersection numbers on the Rapoport--Zink space associated to $\mathcal{X}_0(N)^{2}$ and the derivatives of local representation densities of quadratic forms.

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Qiao He, Baiqing Zhu. 2025-02-26. Intersections of Hecke correspondences on modular curves. https://arxiv.org/abs/2502.19600

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