{"title":"Dirichlet L‐函数的分布","authors":"Zikang Dong, Weijia Wang, Hao Zhang","doi":"10.1112/mtk.12205","DOIUrl":null,"url":null,"abstract":"<p>In this article, we study the distribution of values of Dirichlet <i>L</i>-functions, the distribution of values of the random models for Dirichlet <i>L</i>-functions, and the discrepancy between these two kinds of distributions. For each question, we consider the cases of <math>\n <semantics>\n <mrow>\n <mfrac>\n <mn>1</mn>\n <mn>2</mn>\n </mfrac>\n <mo><</mo>\n <mo>Re</mo>\n <mi>s</mi>\n <mo><</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$\\frac{1}{2}<\\operatorname{Re}s<1$</annotation>\n </semantics></math> and <math>\n <semantics>\n <mrow>\n <mo>Re</mo>\n <mi>s</mi>\n <mo>=</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$\\operatorname{Re}s=1$</annotation>\n </semantics></math> separately.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Distribution of Dirichlet L-functions\",\"authors\":\"Zikang Dong, Weijia Wang, Hao Zhang\",\"doi\":\"10.1112/mtk.12205\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this article, we study the distribution of values of Dirichlet <i>L</i>-functions, the distribution of values of the random models for Dirichlet <i>L</i>-functions, and the discrepancy between these two kinds of distributions. For each question, we consider the cases of <math>\\n <semantics>\\n <mrow>\\n <mfrac>\\n <mn>1</mn>\\n <mn>2</mn>\\n </mfrac>\\n <mo><</mo>\\n <mo>Re</mo>\\n <mi>s</mi>\\n <mo><</mo>\\n <mn>1</mn>\\n </mrow>\\n <annotation>$\\\\frac{1}{2}<\\\\operatorname{Re}s<1$</annotation>\\n </semantics></math> and <math>\\n <semantics>\\n <mrow>\\n <mo>Re</mo>\\n <mi>s</mi>\\n <mo>=</mo>\\n <mn>1</mn>\\n </mrow>\\n <annotation>$\\\\operatorname{Re}s=1$</annotation>\\n </semantics></math> separately.</p>\",\"PeriodicalId\":18463,\"journal\":{\"name\":\"Mathematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-05-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematika\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12205\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematika","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12205","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this article, we study the distribution of values of Dirichlet L-functions, the distribution of values of the random models for Dirichlet L-functions, and the discrepancy between these two kinds of distributions. For each question, we consider the cases of and separately.
期刊介绍：
Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.
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