Airy矩的Hodge性质

IF 0.8 Q2 MATHEMATICS
C. Sabbah, Jeng-Daw Yu
{"title":"Airy矩的Hodge性质","authors":"C. Sabbah, Jeng-Daw Yu","doi":"10.2140/tunis.2023.5.215","DOIUrl":null,"url":null,"abstract":"We consider the complex analogues of symmetric power moments of cubic exponential sums. These are symmetric powers of the classical Airy differential equation. We show that their de Rham cohomologies underlie an arithmetic Hodge structure in the sense of Anderson and we compute their Hodge numbers by means of the irregular Hodge filtration, which is indexed by rational numbers, on their realizations as exponential mixed Hodge structures. The main result is that all Hodge numbers are either zero or one.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2021-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Hodge properties of Airy moments\",\"authors\":\"C. Sabbah, Jeng-Daw Yu\",\"doi\":\"10.2140/tunis.2023.5.215\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the complex analogues of symmetric power moments of cubic exponential sums. These are symmetric powers of the classical Airy differential equation. We show that their de Rham cohomologies underlie an arithmetic Hodge structure in the sense of Anderson and we compute their Hodge numbers by means of the irregular Hodge filtration, which is indexed by rational numbers, on their realizations as exponential mixed Hodge structures. The main result is that all Hodge numbers are either zero or one.\",\"PeriodicalId\":36030,\"journal\":{\"name\":\"Tunisian Journal of Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-12-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tunisian Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/tunis.2023.5.215\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tunisian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/tunis.2023.5.215","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2

摘要

我们考虑三次指数和的对称幂矩的复类似物。这些是经典艾里微分方程的对称幂。我们证明了他们的de Rham上同调是Anderson意义上的算术Hodge结构的基础,并且我们通过由有理数索引的不规则Hodge滤波来计算他们的Hodge数,在他们实现为指数混合Hodge结构时。主要结果是所有的霍奇数要么是零要么是一。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Hodge properties of Airy moments
We consider the complex analogues of symmetric power moments of cubic exponential sums. These are symmetric powers of the classical Airy differential equation. We show that their de Rham cohomologies underlie an arithmetic Hodge structure in the sense of Anderson and we compute their Hodge numbers by means of the irregular Hodge filtration, which is indexed by rational numbers, on their realizations as exponential mixed Hodge structures. The main result is that all Hodge numbers are either zero or one.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Tunisian Journal of Mathematics
Tunisian Journal of Mathematics Mathematics-Mathematics (all)
CiteScore
1.70
自引率
0.00%
发文量
12
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信