[{"date_updated":"2024-10-22T14:43:13Z","volume":146,"author":[{"first_name":"Fabian","full_name":"Januszewski, Fabian","id":"81636","orcid":"0000-0002-3184-237X","last_name":"Januszewski"}],"page":"495-578","intvolume":"       146","citation":{"bibtex":"@article{Januszewski_2024, title={Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central $L$-values}, volume={146}, number={2}, journal={American Journal of Mathematics}, publisher={Johns Hopkins University, Johns Hopkins University Press}, author={Januszewski, Fabian}, year={2024}, pages={495–578} }","mla":"Januszewski, Fabian. “Non-Abelian $p$-Adic Rankin-Selberg $L$-Functions and Non-Vanishing of  Central $L$-Values.” <i>American Journal of Mathematics</i>, vol. 146, no. 2, Johns Hopkins University, Johns Hopkins University Press, 2024, pp. 495–578.","short":"F. Januszewski, American Journal of Mathematics 146 (2024) 495–578.","apa":"Januszewski, F. (2024). Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central $L$-values. <i>American Journal of Mathematics</i>, <i>146</i>(2), 495–578.","chicago":"Januszewski, Fabian. “Non-Abelian $p$-Adic Rankin-Selberg $L$-Functions and Non-Vanishing of  Central $L$-Values.” <i>American Journal of Mathematics</i> 146, no. 2 (2024): 495–578.","ieee":"F. Januszewski, “Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central $L$-values,” <i>American Journal of Mathematics</i>, vol. 146, no. 2, pp. 495–578, 2024.","ama":"Januszewski F. Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central $L$-values. <i>American Journal of Mathematics</i>. 2024;146(2):495-578."},"publication_identifier":{"issn":["0002-9327"]},"publication_status":"published","article_type":"original","_id":"53190","user_id":"81636","status":"public","type":"journal_article","title":"Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central $L$-values","publisher":"Johns Hopkins University, Johns Hopkins University Press","date_created":"2024-04-03T16:55:16Z","year":"2024","issue":"2","language":[{"iso":"eng"}],"external_id":{"arxiv":["1708.02616"]},"abstract":[{"lang":"eng","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."}],"publication":"American Journal of Mathematics"}]