[{"user_id":"81636","_id":"53192","article_type":"original","type":"journal_article","status":"public","author":[{"first_name":"Mladen","last_name":"Dimitrov","full_name":"Dimitrov, Mladen"},{"first_name":"Fabian","last_name":"Januszewski","full_name":"Januszewski, Fabian","id":"81636"},{"first_name":"A.","last_name":"Raghuram","full_name":"Raghuram, A."}],"volume":156,"date_updated":"2024-04-03T17:13:25Z","doi":"10.1112/s0010437x20007551","publication_status":"published","publication_identifier":{"issn":["0010-437X","1570-5846"]},"citation":{"bibtex":"@article{Dimitrov_Januszewski_Raghuram_2021, title={L-functions of GL(2n): p-adic properties and non-vanishing of twists}, volume={156}, DOI={10.1112/s0010437x20007551}, number={12}, journal={Compositio Mathematica}, publisher={Wiley}, author={Dimitrov, Mladen and Januszewski, Fabian and Raghuram, A.}, year={2021}, pages={2437–2468} }","short":"M. Dimitrov, F. Januszewski, A. Raghuram, Compositio Mathematica 156 (2021) 2437–2468.","mla":"Dimitrov, Mladen, et al. “L-Functions of GL(2n): P-Adic Properties and Non-Vanishing of Twists.” Compositio Mathematica, vol. 156, no. 12, Wiley, 2021, pp. 2437–68, doi:10.1112/s0010437x20007551.","apa":"Dimitrov, M., Januszewski, F., & Raghuram, A. (2021). L-functions of GL(2n): p-adic properties and non-vanishing of twists. Compositio Mathematica, 156(12), 2437–2468. https://doi.org/10.1112/s0010437x20007551","ama":"Dimitrov M, Januszewski F, Raghuram A. L-functions of GL(2n): p-adic properties and non-vanishing of twists. Compositio Mathematica. 2021;156(12):2437-2468. doi:10.1112/s0010437x20007551","chicago":"Dimitrov, Mladen, Fabian Januszewski, and A. Raghuram. “L-Functions of GL(2n): P-Adic Properties and Non-Vanishing of Twists.” Compositio Mathematica 156, no. 12 (2021): 2437–68. https://doi.org/10.1112/s0010437x20007551.","ieee":"M. Dimitrov, F. Januszewski, and A. Raghuram, “L-functions of GL(2n): p-adic properties and non-vanishing of twists,” Compositio Mathematica, vol. 156, no. 12, pp. 2437–2468, 2021, doi: 10.1112/s0010437x20007551."},"intvolume":" 156","page":"2437-2468","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"publication":"Compositio Mathematica","abstract":[{"text":"The principal aim of this article is to attach and study $p$-adic $L$-functions to cohomological cuspidal automorphic representations $\\Pi$ of $\\operatorname {GL}_{2n}$ over a totally real field $F$ admitting a Shalika model. We use a modular symbol approach, along the global lines of the work of Ash and Ginzburg, but our results are more definitive because we draw heavily upon the methods used in the recent and separate works of all three authors. By construction, our $p$-adic $L$-functions are distributions on the Galois group of the maximal abelian extension of $F$ unramified outside $p\\infty$. Moreover, we work under a weaker Panchishkine-type condition on $\\Pi _p$ rather than the full ordinariness condition. Finally, we prove the so-called Manin relations between the $p$-adic $L$-functions at all critical points. This has the striking consequence that, given a unitary $\\Pi$ whose standard $L$-function admits at least two critical points, and given a prime $p$ such that $\\Pi _p$ is ordinary, the central critical value $L(\\frac {1}{2}, \\Pi \\otimes \\chi )$ is non-zero for all except finitely many Dirichlet characters $\\chi$ of $p$-power conductor.","lang":"eng"}],"date_created":"2024-04-03T16:58:55Z","publisher":"Wiley","title":"L-functions of GL(2n): p-adic properties and non-vanishing of twists","issue":"12","year":"2021"},{"language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"department":[{"_id":"555"}],"user_id":"93826","_id":"37672","status":"public","abstract":[{"text":"AbstractLet ${F}_{BC} (\\lambda , k; t)$ be the Heckman–Opdam hypergeometric function of type BC with multiplicities $k= ({k}_{1} , {k}_{2} , {k}_{3} )$ and weighted half-sum $\\rho (k)$ of positive roots. We prove that ${F}_{BC} (\\lambda + \\rho (k), k; t)$ converges as ${k}_{1} + {k}_{2} \\rightarrow \\infty $ and ${k}_{1} / {k}_{2} \\rightarrow \\infty $ to a function of type A for $t\\in { \\mathbb{R} }^{n} $ and $\\lambda \\in { \\mathbb{C} }^{n} $. This limit is obtained from a corresponding result for Jacobi polynomials of type BC, which is proven for a slightly more general limit behavior of the multiplicities, using an explicit representation of Jacobi polynomials in terms of Jack polynomials. Our limits include limit transitions for the spherical functions of non-compact Grassmann manifolds over one of the fields $ \\mathbb{F} = \\mathbb{R} , \\mathbb{C} , \\mathbb{H} $ when the rank is fixed and the dimension tends to infinity. The limit functions turn out to be exactly the spherical functions of the corresponding infinite-dimensional Grassmann manifold in the sense of Olshanski.","lang":"eng"}],"publication":"Compositio Mathematica","type":"journal_article","doi":"10.1112/s0010437x13007045","title":"Limit transition between hypergeometric functions of type BC and type A","volume":149,"date_created":"2023-01-20T09:37:16Z","author":[{"full_name":"Rösler, Margit","id":"37390","last_name":"Rösler","first_name":"Margit"},{"first_name":"Tom","full_name":"Koornwinder, Tom","last_name":"Koornwinder"},{"full_name":"Voit, Michael","last_name":"Voit","first_name":"Michael"}],"publisher":"Wiley","date_updated":"2023-01-24T22:15:13Z","page":"1381-1400","intvolume":" 149","citation":{"ama":"Rösler M, Koornwinder T, Voit M. Limit transition between hypergeometric functions of type BC and type A. Compositio Mathematica. 2013;149(8):1381-1400. doi:10.1112/s0010437x13007045","chicago":"Rösler, Margit, Tom Koornwinder, and Michael Voit. “Limit Transition between Hypergeometric Functions of Type BC and Type A.” Compositio Mathematica 149, no. 8 (2013): 1381–1400. https://doi.org/10.1112/s0010437x13007045.","ieee":"M. Rösler, T. Koornwinder, and M. Voit, “Limit transition between hypergeometric functions of type BC and type A,” Compositio Mathematica, vol. 149, no. 8, pp. 1381–1400, 2013, doi: 10.1112/s0010437x13007045.","apa":"Rösler, M., Koornwinder, T., & Voit, M. (2013). Limit transition between hypergeometric functions of type BC and type A. Compositio Mathematica, 149(8), 1381–1400. https://doi.org/10.1112/s0010437x13007045","short":"M. Rösler, T. Koornwinder, M. Voit, Compositio Mathematica 149 (2013) 1381–1400.","mla":"Rösler, Margit, et al. “Limit Transition between Hypergeometric Functions of Type BC and Type A.” Compositio Mathematica, vol. 149, no. 8, Wiley, 2013, pp. 1381–400, doi:10.1112/s0010437x13007045.","bibtex":"@article{Rösler_Koornwinder_Voit_2013, title={Limit transition between hypergeometric functions of type BC and type A}, volume={149}, DOI={10.1112/s0010437x13007045}, number={8}, journal={Compositio Mathematica}, publisher={Wiley}, author={Rösler, Margit and Koornwinder, Tom and Voit, Michael}, year={2013}, pages={1381–1400} }"},"year":"2013","issue":"8","publication_identifier":{"issn":["0010-437X","1570-5846"]},"publication_status":"published"},{"date_created":"2023-01-25T09:55:18Z","publisher":"Wiley","title":"Bessel convolutions on matrix cones","issue":"03","year":"2007","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"publication":"Compositio Mathematica","volume":143,"author":[{"first_name":"Margit","last_name":"Rösler","id":"37390","full_name":"Rösler, Margit"}],"date_updated":"2023-01-26T17:47:42Z","doi":"10.1112/s0010437x06002594","publication_identifier":{"issn":["0010-437X","1570-5846"]},"publication_status":"published","page":"749-779","intvolume":" 143","citation":{"apa":"Rösler, M. (2007). Bessel convolutions on matrix cones. Compositio Mathematica, 143(03), 749–779. https://doi.org/10.1112/s0010437x06002594","bibtex":"@article{Rösler_2007, title={Bessel convolutions on matrix cones}, volume={143}, DOI={10.1112/s0010437x06002594}, number={03}, journal={Compositio Mathematica}, publisher={Wiley}, author={Rösler, Margit}, year={2007}, pages={749–779} }","mla":"Rösler, Margit. “Bessel Convolutions on Matrix Cones.” Compositio Mathematica, vol. 143, no. 03, Wiley, 2007, pp. 749–79, doi:10.1112/s0010437x06002594.","short":"M. Rösler, Compositio Mathematica 143 (2007) 749–779.","chicago":"Rösler, Margit. “Bessel Convolutions on Matrix Cones.” Compositio Mathematica 143, no. 03 (2007): 749–79. https://doi.org/10.1112/s0010437x06002594.","ieee":"M. Rösler, “Bessel convolutions on matrix cones,” Compositio Mathematica, vol. 143, no. 03, pp. 749–779, 2007, doi: 10.1112/s0010437x06002594.","ama":"Rösler M. Bessel convolutions on matrix cones. Compositio Mathematica. 2007;143(03):749-779. doi:10.1112/s0010437x06002594"},"department":[{"_id":"555"}],"user_id":"93826","_id":"39947","extern":"1","type":"journal_article","status":"public"}]