{"date_updated":"2024-04-03T17:14:52Z","page":"65","language":[{"iso":"eng"}],"abstract":[{"text":"We study Hecke algebras for pairs $({\\mathfrak g},K)$ over arbitrary fields\r\n$E$ of characteristic $0$, define the Bernstein functor and give another\r\ndefinition of the Zuckerman functor over $E$. Building on this and the author's\r\nprevious work on rational structures on automorphic representations, we show\r\nthat hard duality remains valid over $E$ and apply this result to the study of\r\nrationality properties of Sun's cohomologically induced functionals. Our main\r\napplication are period relations for the special values of standard\r\n$L$-functions of automorphic representations of $\\mathrm{GL}(2n)$ admitting\r\nShalika models.","lang":"eng"}],"publication":"arXiv:1604.04253","title":"On Period Relations for Automorphic L-functions II","user_id":"81636","author":[{"id":"81636","first_name":"Fabian","last_name":"Januszewski","full_name":"Januszewski, Fabian"}],"year":"2016","status":"public","_id":"53196","publication_status":"submitted","external_id":{"arxiv":["1604.04253"]},"date_created":"2024-04-03T17:13:55Z","citation":{"mla":"Januszewski, Fabian. “On Period Relations for Automorphic L-Functions II.” <i>ArXiv:1604.04253</i>.","chicago":"Januszewski, Fabian. “On Period Relations for Automorphic L-Functions II.” <i>ArXiv:1604.04253</i>, n.d.","apa":"Januszewski, F. (n.d.). On Period Relations for Automorphic L-functions II. In <i>arXiv:1604.04253</i>.","short":"F. Januszewski, ArXiv:1604.04253 (n.d.).","bibtex":"@article{Januszewski, title={On Period Relations for Automorphic L-functions II}, journal={arXiv:1604.04253}, author={Januszewski, Fabian} }","ieee":"F. Januszewski, “On Period Relations for Automorphic L-functions II,” <i>arXiv:1604.04253</i>. .","ama":"Januszewski F. On Period Relations for Automorphic L-functions II. <i>arXiv:160404253</i>."},"type":"preprint"}