在kaneko和koike之后的极值拟模形式

Pub Date : 2019-10-25 DOI:10.2206/kyushujm.74.401

F. Pellarin, G. Nebe

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引用次数: 8

摘要

Kaneko和Koike引入了极值拟模形式的概念，并对其算术性质提出了猜想。本文的目的是证明这些准模形式的一个相当尖锐的重性估计。笔记以围绕这些猜想的讨论和部分答案结束，G. Nebe的附录包含了权值14和深度1的归一化极值拟模形式的傅里叶系数的完整性证明。

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ON EXTREMAL QUASI-MODULAR FORMS AFTER KANEKO AND KOIKE

Kaneko and Koike introduced the notion of extremal quasi-modular form and proposed conjectures on their arithmetic properties. The aim of this note is to prove a rather sharp multiplicity estimate for these quasi-modular forms. The note ends with discussions and partial answers around these conjectures and an appendix by G. Nebe containing the proof of the integrality of the Fourier coefficients of the normalised extremal quasimodular form of weight 14 and depth 1.

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