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arXiv · 2509.24363

Modular Heights of Unitary Shimura Varieties I: Derivatives of Eisenstein Series

Ziqi Guo
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Abstract

This is the first of a series of three papers, in which we prove a formula expressing the modular height of a unitary Shimura variety over a CM number field in terms of the logarithmic derivative of the Hecke L-function associated with the CM extension. The main idea of our proof is to compare the holomorphic projection of the derivative of a certain mixed Eisenstein-theta series and the arithmetic degree of a generating series of divisors on unitary Shimura varieties. In this paper, we compute an explicit expression of the holomorphic projection of the derivative of a certain mixed Eisenstein-theta series.

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Ziqi Guo. 2025-09-29. Modular Heights of Unitary Shimura Varieties I: Derivatives of Eisenstein Series. https://arxiv.org/abs/2509.24363

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