{"title":"椭圆上的Kloosterman和","authors":"Sergey Varbanets, Yakov Vorobyov","doi":"10.12958/adm2048","DOIUrl":null,"url":null,"abstract":"The main point of our research is to obtain the estimates for Kloosterman sums K(α, β; h, q; k) considered on the ellipse bound for the case of the integer rational moduleq and forsome natural number k with conditions (α, q)=(β, q)=1 on the integer numbers of imaginary quadratic field. These estimates can be used to construct the asymptotic formulas for the sum of divisors function τℓ(α)forℓ= 2,3, . . . over the ring of integer elements of imaginary quadratic field in arithmetic progression.","PeriodicalId":364397,"journal":{"name":"Algebra and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Kloosterman sums on the ellipse\",\"authors\":\"Sergey Varbanets, Yakov Vorobyov\",\"doi\":\"10.12958/adm2048\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The main point of our research is to obtain the estimates for Kloosterman sums K(α, β; h, q; k) considered on the ellipse bound for the case of the integer rational moduleq and forsome natural number k with conditions (α, q)=(β, q)=1 on the integer numbers of imaginary quadratic field. These estimates can be used to construct the asymptotic formulas for the sum of divisors function τℓ(α)forℓ= 2,3, . . . over the ring of integer elements of imaginary quadratic field in arithmetic progression.\",\"PeriodicalId\":364397,\"journal\":{\"name\":\"Algebra and Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra and Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12958/adm2048\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra and Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12958/adm2048","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The main point of our research is to obtain the estimates for Kloosterman sums K(α, β; h, q; k) considered on the ellipse bound for the case of the integer rational moduleq and forsome natural number k with conditions (α, q)=(β, q)=1 on the integer numbers of imaginary quadratic field. These estimates can be used to construct the asymptotic formulas for the sum of divisors function τℓ(α)forℓ= 2,3, . . . over the ring of integer elements of imaginary quadratic field in arithmetic progression.
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