乘性函数与幂序列的不相关及其在自同构L-函数系数上的应用

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2022-12-27 DOI:10.1112/mtk.12182

Xiaoguang He, Mengdi Wang

{"title":"乘性函数与幂序列的不相关及其在自同构L-函数系数上的应用","authors":"Xiaoguang He, Mengdi Wang","doi":"10.1112/mtk.12182","DOIUrl":null,"url":null,"abstract":"We introduce a class of multiplicative functions in which each function satisfies some statistic conditions, and then prove that the above functions are not correlated with finite degree polynomial nilsequences. Besides, we give two applications of this result. One is that the twisting of coefficients of automorphic L-function on <math>\n <semantics>\n <mrow>\n <mi>G</mi>\n <msub>\n <mi>L</mi>\n <mi>m</mi>\n </msub>\n <mrow>\n <mo>(</mo>\n <mi>m</mi>\n <mo>⩾</mo>\n <mn>2</mn>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$GL_m (m \\geqslant 2)$</annotation>\n </semantics></math> and polynomial nilsequences has logarithmic decay; the other is that the mean value of the Möbius function, coefficients of automorphic L-function, and polynomial nilsequences also has logarithmic decay.","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12182","citationCount":"1","resultStr":"{\"title\":\"Discorrelation of multiplicative functions with nilsequences and its application on coefficients of automorphic L-functions\",\"authors\":\"Xiaoguang He, Mengdi Wang\",\"doi\":\"10.1112/mtk.12182\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a class of multiplicative functions in which each function satisfies some statistic conditions, and then prove that the above functions are not correlated with finite degree polynomial nilsequences. Besides, we give two applications of this result. One is that the twisting of coefficients of automorphic L-function on <math>\\n <semantics>\\n <mrow>\\n <mi>G</mi>\\n <msub>\\n <mi>L</mi>\\n <mi>m</mi>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <mi>m</mi>\\n <mo>⩾</mo>\\n <mn>2</mn>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$GL_m (m \\\\geqslant 2)$</annotation>\\n </semantics></math> and polynomial nilsequences has logarithmic decay; the other is that the mean value of the Möbius function, coefficients of automorphic L-function, and polynomial nilsequences also has logarithmic decay.\",\"PeriodicalId\":18463,\"journal\":{\"name\":\"Mathematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2022-12-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12182\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematika\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12182\",\"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.12182","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

我们引入了一类乘法函数，其中每个函数都满足一些统计条件，然后证明了上述函数与有限次多项式幂序列不相关。此外，我们还给出了这一结果的两个应用。一个是自同构L-函数在GLm（m⩾2）$GL_m（m \geqslant 2）$和多项式幂序列上的系数的扭曲具有对数衰减；另一个是Möbius函数的均值、自同构L‐函数的系数和多项式幂序列也具有对数衰减。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Discorrelation of multiplicative functions with nilsequences and its application on coefficients of automorphic L-functions

We introduce a class of multiplicative functions in which each function satisfies some statistic conditions, and then prove that the above functions are not correlated with finite degree polynomial nilsequences. Besides, we give two applications of this result. One is that the twisting of coefficients of automorphic L-function on $G L_{m} (m ⩾ 2)$ and polynomial nilsequences has logarithmic decay; the other is that the mean value of the Möbius function, coefficients of automorphic L-function, and polynomial nilsequences also has logarithmic decay.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

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.