{"title":"Chebyshev对Ramanujan 's $\\tau$-函数的偏差通过深度黎曼假设","authors":"S. Koyama, N. Kurokawa","doi":"10.3792/pjaa.98.007","DOIUrl":null,"url":null,"abstract":"The authors assume the Deep Riemann Hypothesis to prove that a weighted sum of Ramanujan’s τ -function has a bias to being positive. This phenomenon is an analogue of Chebyshev’s bias.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Chebyshev’s bias for Ramanujan’s $\\\\tau$-function via the Deep Riemann Hypothesis\",\"authors\":\"S. Koyama, N. Kurokawa\",\"doi\":\"10.3792/pjaa.98.007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The authors assume the Deep Riemann Hypothesis to prove that a weighted sum of Ramanujan’s τ -function has a bias to being positive. This phenomenon is an analogue of Chebyshev’s bias.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-03-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3792/pjaa.98.007\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3792/pjaa.98.007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Chebyshev’s bias for Ramanujan’s $\tau$-function via the Deep Riemann Hypothesis
The authors assume the Deep Riemann Hypothesis to prove that a weighted sum of Ramanujan’s τ -function has a bias to being positive. This phenomenon is an analogue of Chebyshev’s bias.
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