{"title":"Covering of elliptic curves and Fuchsian equations","authors":"A. Smirnov","doi":"10.1109/DD46733.2019.9016464","DOIUrl":null,"url":null,"abstract":"The paper presents a method for constructing hyperelliptic integrals that are reducible to elliptic. Picard–Fuchs equations for integrals of known reducible hyperelliptic differentials are found. Numerous examples of reducible hyperelliptic integrals of the first and the second kind, and examples of Picard–Fuchs equations that have solutions in the form of hyperelliptic integrals are given.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"85 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2019 Days on Diffraction (DD)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/DD46733.2019.9016464","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
The paper presents a method for constructing hyperelliptic integrals that are reducible to elliptic. Picard–Fuchs equations for integrals of known reducible hyperelliptic differentials are found. Numerous examples of reducible hyperelliptic integrals of the first and the second kind, and examples of Picard–Fuchs equations that have solutions in the form of hyperelliptic integrals are given.
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