EXTREMAL QUASIMODULAR FORMS OF LOWER DEPTH WITH INTEGRAL FOURIER COEFFICIENTS

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2021-01-25 DOI:10.2206/kyushujm.75.351

Tsudoi Kaminaka, Fumiharu Kato

引用次数: 1

Abstract

We show that, based on Grabner’s recent results on modular differential equations satisfied by quasimodular forms, there exist only finitely many normalized extremal quasimodular forms of depth r that have all Fourier coefficients integral for each of r = 1, 2, 3, 4, and partly classifies them, where the classification is complete for r = 2, 3, 4; in fact, we show that there exists no normalized extremal quasimodular forms of depth 4 with all Fourier coefficients integral. Our result disproves a conjecture by Pellarin.

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具有积分傅立叶系数的下深度极值拟模形式

基于Grabner关于准模形式满足的模微分方程的最新结果，我们证明了深度r的归一化极值拟模形式只存在有限多个，它们对r = 1,2,3,4的傅里叶系数都是积分的，并对它们进行了部分分类，其中对r = 2,3,4的分类是完全的;事实上，我们证明了深度4的归一化极值拟模形式不存在，且所有的傅里叶系数都是积分的。我们的结果反驳了佩拉林的一个猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.