{"title":"ON EXTREMAL QUASI-MODULAR FORMS AFTER KANEKO AND KOIKE","authors":"F. Pellarin, G. Nebe","doi":"10.2206/kyushujm.74.401","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2019-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kyushu Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2206/kyushujm.74.401","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 8
Abstract
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.
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.
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