{"title":"论黎曼 Zeta 函数零点序列中的线性形式","authors":"E. D. Yudelevich","doi":"10.1134/s0001434624010103","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We obtain an asymptotic formula for the sum </p><span>$$H=\\sum_{0<\\gamma_k\\le T,\\,1\\le k\\le 4}h(\\gamma_1+\\gamma_2-\\gamma_3-\\gamma_4),$$</span><p> where the <span>\\(\\gamma_k\\)</span> run over the imaginary parts of nontrivial zeros of the Riemann zeta function with multiplicities taken into account and the function <span>\\(h\\)</span> belongs to some special class of functions in <span>\\(L^1(\\mathbb R)\\)</span>. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a Linear Form in the Ordinates of Zeros of the Riemann Zeta Function\",\"authors\":\"E. D. Yudelevich\",\"doi\":\"10.1134/s0001434624010103\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> We obtain an asymptotic formula for the sum </p><span>$$H=\\\\sum_{0<\\\\gamma_k\\\\le T,\\\\,1\\\\le k\\\\le 4}h(\\\\gamma_1+\\\\gamma_2-\\\\gamma_3-\\\\gamma_4),$$</span><p> where the <span>\\\\(\\\\gamma_k\\\\)</span> run over the imaginary parts of nontrivial zeros of the Riemann zeta function with multiplicities taken into account and the function <span>\\\\(h\\\\)</span> belongs to some special class of functions in <span>\\\\(L^1(\\\\mathbb R)\\\\)</span>. </p>\",\"PeriodicalId\":18294,\"journal\":{\"name\":\"Mathematical Notes\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Notes\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0001434624010103\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0001434624010103","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
where the \(\gamma_k\) run over the imaginary parts of nontrivial zeros of the Riemann zeta function with multiplicities taken into account and the function \(h\) belongs to some special class of functions in \(L^1(\mathbb R)\).
期刊介绍：
Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.
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