{"title":"Linear dependence of quasi-periods over the rationals","authors":"K. S. Kumar","doi":"10.5802/CRMATH.171","DOIUrl":null,"url":null,"abstract":"In this note we shall show that a lattice Zω1 +Zω2 in C has Q-linearly dependent quasi-periods if and only if ω2/ω1 is equivalent to a zero of the Eisenstein series E2 under the action of SL2(Z) on the upper half plane of C. 2020 Mathematics Subject Classification. 11J72, 11J89. Manuscript received 23rd March 2020, revised 7th August 2020, accepted 17th December 2020.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":"14 1","pages":"409-414"},"PeriodicalIF":0.8000,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus Mathematique","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/CRMATH.171","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this note we shall show that a lattice Zω1 +Zω2 in C has Q-linearly dependent quasi-periods if and only if ω2/ω1 is equivalent to a zero of the Eisenstein series E2 under the action of SL2(Z) on the upper half plane of C. 2020 Mathematics Subject Classification. 11J72, 11J89. Manuscript received 23rd March 2020, revised 7th August 2020, accepted 17th December 2020.
期刊介绍：
The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, …
Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English.
The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.
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