{"title":"临界带边缘上Rankin-Selberg $L$-函数的下界","authors":"Qiao Zhang","doi":"10.4064/aa221111-14-7","DOIUrl":null,"url":null,"abstract":"Let $F$ be a number field, and let $\\pi_1$ and $\\pi_2$ be distinct unitary cuspidal automorphic representations of $\\operatorname{GL}_{n_1}(\\mathbb{A}_F)$ and $\\operatorname{GL}_{n_2}(\\mathbb{A}_F)$ respectively. In this paper, we derive new lower bounds for the Rankin-Selberg $L$-function $L(s, \\pi_1 \\times \\widetilde{\\pi}_2)$ along the edge $\\Re s = 1$ of the critical strip in the $t$-aspect. The corresponding zero-free region for $L(s, \\pi_1 \\times \\widetilde{\\pi}_2)$ is also determined.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"112 1","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lower bounds for Rankin–Selberg $L$-functions on the edge of the critical strip\",\"authors\":\"Qiao Zhang\",\"doi\":\"10.4064/aa221111-14-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $F$ be a number field, and let $\\\\pi_1$ and $\\\\pi_2$ be distinct unitary cuspidal automorphic representations of $\\\\operatorname{GL}_{n_1}(\\\\mathbb{A}_F)$ and $\\\\operatorname{GL}_{n_2}(\\\\mathbb{A}_F)$ respectively. In this paper, we derive new lower bounds for the Rankin-Selberg $L$-function $L(s, \\\\pi_1 \\\\times \\\\widetilde{\\\\pi}_2)$ along the edge $\\\\Re s = 1$ of the critical strip in the $t$-aspect. The corresponding zero-free region for $L(s, \\\\pi_1 \\\\times \\\\widetilde{\\\\pi}_2)$ is also determined.\",\"PeriodicalId\":37888,\"journal\":{\"name\":\"Acta Arithmetica\",\"volume\":\"112 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Arithmetica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4064/aa221111-14-7\",\"RegionNum\":3,\"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":"Acta Arithmetica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4064/aa221111-14-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Lower bounds for Rankin–Selberg $L$-functions on the edge of the critical strip
Let $F$ be a number field, and let $\pi_1$ and $\pi_2$ be distinct unitary cuspidal automorphic representations of $\operatorname{GL}_{n_1}(\mathbb{A}_F)$ and $\operatorname{GL}_{n_2}(\mathbb{A}_F)$ respectively. In this paper, we derive new lower bounds for the Rankin-Selberg $L$-function $L(s, \pi_1 \times \widetilde{\pi}_2)$ along the edge $\Re s = 1$ of the critical strip in the $t$-aspect. The corresponding zero-free region for $L(s, \pi_1 \times \widetilde{\pi}_2)$ is also determined.