{"title":"Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central $L$-values","publication":"To appear in the American Journal of Mathematics","abstract":[{"text":"We prove new congruences between special values of Rankin-Selberg\r\n$L$-functions for $\\mathrm{GL}(n+1)\\times\\mathrm{GL}(n)$ over arbitrary number\r\nfields. This allows us to control the behavior of $p$-adic $L$-functions under\r\nTate twists and to prove the existence of non-abelian $p$-adic $L$-functions\r\nfor Hida families on $\\mathrm{GL}(n+1)\\times\\mathrm{GL}(n)$. As an application,\r\nwe prove strong non-vanishing results for central $L$-values: We give\r\nsufficient local conditions for twisted central Rankin-Selberg $L$-values to be\r\ngenerically non-zero.","lang":"eng"}],"language":[{"iso":"eng"}],"date_updated":"2024-04-03T17:13:33Z","citation":{"short":"F. Januszewski, To Appear in the American Journal of Mathematics (n.d.).","bibtex":"@article{Januszewski, title={Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central $L$-values}, journal={To appear in the American Journal of Mathematics}, publisher={Johns Hopkins University, Johns Hopkins University Press}, author={Januszewski, Fabian} }","ieee":"F. Januszewski, “Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central $L$-values,” <i>To appear in the American Journal of Mathematics</i>.","ama":"Januszewski F. Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central $L$-values. <i>To appear in the American Journal of Mathematics</i>.","mla":"Januszewski, Fabian. “Non-Abelian $p$-Adic Rankin-Selberg $L$-Functions and Non-Vanishing of  Central $L$-Values.” <i>To Appear in the American Journal of Mathematics</i>, Johns Hopkins University, Johns Hopkins University Press.","chicago":"Januszewski, Fabian. “Non-Abelian $p$-Adic Rankin-Selberg $L$-Functions and Non-Vanishing of  Central $L$-Values.” <i>To Appear in the American Journal of Mathematics</i>, n.d.","apa":"Januszewski, F. (n.d.). Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central $L$-values. <i>To Appear in the American Journal of Mathematics</i>."},"publisher":"Johns Hopkins University, Johns Hopkins University Press","type":"journal_article","_id":"53190","status":"public","date_created":"2024-04-03T16:55:16Z","article_type":"original","publication_status":"inpress","external_id":{"arxiv":["1708.02616"]},"year":"2024","author":[{"full_name":"Januszewski, Fabian","last_name":"Januszewski","first_name":"Fabian","id":"81636"}],"user_id":"81636","publication_identifier":{"issn":["0002-9327"]}}