{"title":"A generalization of Siegel’s method to Jacobi’s $$\\vartheta _1$$ function","authors":"Maher Mamah, Ali Saraeb","doi":"10.1007/s11139-024-00894-7","DOIUrl":null,"url":null,"abstract":"<p>We present a new proof of the transformation law of <span>\\(\\vartheta _1\\)</span> under the action of the generator of the full modular group <span>\\(\\Gamma \\)</span> using Siegel’s method.</p>","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":"23 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Ramanujan Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11139-024-00894-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We present a new proof of the transformation law of \(\vartheta _1\) under the action of the generator of the full modular group \(\Gamma \) using Siegel’s method.
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