{"title":"西格尔方法对雅各比$$\\vartheta _1$$函数的推广","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":"{\"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}","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}
A generalization of Siegel’s method to Jacobi’s $$\vartheta _1$$ function
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.