{"publication_status":"inpress","author":[{"last_name":"Januszewski","full_name":"Januszewski, Fabian","id":"81636","first_name":"Fabian"}],"external_id":{"arxiv":["1708.02616"]},"type":"journal_article","language":[{"iso":"eng"}],"publisher":"Johns Hopkins University, Johns Hopkins University Press","user_id":"81636","publication_identifier":{"issn":["0002-9327"]},"title":"Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-values","year":"2024","date_updated":"2024-04-03T17:13:33Z","status":"public","date_created":"2024-04-03T16:55:16Z","article_type":"original","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"}],"_id":"53190","citation":{"mla":"Januszewski, Fabian. “Non-Abelian $p$-Adic Rankin-Selberg $L$-Functions and Non-Vanishing of Central $L$-Values.” *To Appear in the American Journal of Mathematics*, Johns Hopkins University, Johns Hopkins University Press.","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} }","ama":"Januszewski F. Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-values. *To appear in the American Journal of Mathematics*.","short":"F. Januszewski, To Appear in the American Journal of Mathematics (n.d.).","apa":"Januszewski, F. (n.d.). Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-values. *To Appear in the American Journal of Mathematics*.","chicago":"Januszewski, Fabian. “Non-Abelian $p$-Adic Rankin-Selberg $L$-Functions and Non-Vanishing of Central $L$-Values.” *To Appear in the American Journal of Mathematics*, n.d.","ieee":"F. Januszewski, “Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-values,” *To appear in the American Journal of Mathematics*."},"publication":"To appear in the American Journal of Mathematics"}