Average CM-values of Higher Green's Function and Factorization

Yingkun Li

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arXiv · 1812.08523

Average CM-values of Higher Green's Function and Factorization

Yingkun Li

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Abstract

In this paper, we prove an averaged version of an algebraicity conjecture in \cite{GKZ87} concerning the values of higher Green's function at CM points. Furthermore, we give the factorization of the ideal generated by such algebraic value in the spirit of the famous work of Gross and Zagier on singular moduli.

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Yingkun Li. 2018-12-20. Average CM-values of Higher Green's Function and Factorization. https://arxiv.org/abs/1812.08523

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