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arXiv · 2010.11355

Hurwitz class numbers with level and modular correspondences

Yuya Murakami
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Abstract

In this paper, we prove Hurwitz-Eichler type formulas for Hurwitz class numbers with each level $ M $ when the modular curve $ X_0(M) $ has genus zero. A key idea is to calculate intersection numbers of modular correspondences with the level in two different ways. A generalization of Atkin-Lehner involutions for $ Γ_0(M) $ and its subgroup $ Γ_0^{(M')}(M) $ is introduced to calculate intersection multiplicities of modular correspondences at cusps.

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Yuya Murakami. 2020-10-27. Hurwitz class numbers with level and modular correspondences. https://arxiv.org/abs/2010.11355

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