[{"publication_status":"published","date_updated":"2026-02-19T13:27:34Z","intvolume":"      2022","title":"Ellipticity and discrete series","year":"2021","author":[{"last_name":"Krötz","first_name":"Bernhard","full_name":"Krötz, Bernhard"},{"full_name":"Kuit, Job J.","last_name":"Kuit","first_name":"Job J."},{"first_name":"Eric M.","last_name":"Opdam","full_name":"Opdam, Eric M."},{"full_name":"Schlichtkrull, Henrik","first_name":"Henrik","last_name":"Schlichtkrull"}],"publication_identifier":{"issn":["0075-4102","1435-5345"]},"doi":"10.1515/crelle-2021-0063","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>We explain by elementary means why the existence of a discrete series representation\r\nof a real reductive group <jats:italic>G</jats:italic> implies the existence of a compact Cartan subgroup of <jats:italic>G</jats:italic>. The presented approach has the potential to generalize to real spherical spaces.</jats:p>"}],"publication":"Journal für die reine und angewandte Mathematik (Crelles Journal)","issue":"782","type":"journal_article","date_created":"2026-02-19T13:27:22Z","status":"public","user_id":"52730","volume":2022,"page":"109-119","publisher":"Walter de Gruyter GmbH","_id":"64275","citation":{"chicago":"Krötz, Bernhard, Job J. Kuit, Eric M. Opdam, and Henrik Schlichtkrull. “Ellipticity and Discrete Series.” <i>Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)</i> 2022, no. 782 (2021): 109–19. <a href=\"https://doi.org/10.1515/crelle-2021-0063\">https://doi.org/10.1515/crelle-2021-0063</a>.","short":"B. Krötz, J.J. Kuit, E.M. Opdam, H. Schlichtkrull, Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 2022 (2021) 109–119.","apa":"Krötz, B., Kuit, J. J., Opdam, E. M., &#38; Schlichtkrull, H. (2021). Ellipticity and discrete series. <i>Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)</i>, <i>2022</i>(782), 109–119. <a href=\"https://doi.org/10.1515/crelle-2021-0063\">https://doi.org/10.1515/crelle-2021-0063</a>","ieee":"B. Krötz, J. J. Kuit, E. M. Opdam, and H. Schlichtkrull, “Ellipticity and discrete series,” <i>Journal für die reine und angewandte Mathematik (Crelles Journal)</i>, vol. 2022, no. 782, pp. 109–119, 2021, doi: <a href=\"https://doi.org/10.1515/crelle-2021-0063\">10.1515/crelle-2021-0063</a>.","ama":"Krötz B, Kuit JJ, Opdam EM, Schlichtkrull H. Ellipticity and discrete series. <i>Journal für die reine und angewandte Mathematik (Crelles Journal)</i>. 2021;2022(782):109-119. doi:<a href=\"https://doi.org/10.1515/crelle-2021-0063\">10.1515/crelle-2021-0063</a>","bibtex":"@article{Krötz_Kuit_Opdam_Schlichtkrull_2021, title={Ellipticity and discrete series}, volume={2022}, DOI={<a href=\"https://doi.org/10.1515/crelle-2021-0063\">10.1515/crelle-2021-0063</a>}, number={782}, journal={Journal für die reine und angewandte Mathematik (Crelles Journal)}, publisher={Walter de Gruyter GmbH}, author={Krötz, Bernhard and Kuit, Job J. and Opdam, Eric M. and Schlichtkrull, Henrik}, year={2021}, pages={109–119} }","mla":"Krötz, Bernhard, et al. “Ellipticity and Discrete Series.” <i>Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)</i>, vol. 2022, no. 782, Walter de Gruyter GmbH, 2021, pp. 109–19, doi:<a href=\"https://doi.org/10.1515/crelle-2021-0063\">10.1515/crelle-2021-0063</a>."}},{"date_created":"2024-04-03T16:47:27Z","keyword":["Applied Mathematics","General Mathematics"],"type":"journal_article","issue":"653","publication":"Journal für die reine und angewandte Mathematik (Crelles Journal)","extern":"1","language":[{"iso":"eng"}],"doi":"10.1515/crelle.2011.018","year":"2010","title":"Modular symbols for reductive groups and p-adic Rankin–Selberg convolutions over number fields","author":[{"id":"81636","last_name":"Januszewski","first_name":"Fabian","full_name":"Januszewski, Fabian"}],"publication_identifier":{"issn":["0075-4102","1435-5345"]},"date_updated":"2024-04-03T17:13:10Z","publication_status":"published","intvolume":"      2011","article_type":"original","citation":{"bibtex":"@article{Januszewski_2010, title={Modular symbols for reductive groups and p-adic Rankin–Selberg convolutions over number fields}, volume={2011}, DOI={<a href=\"https://doi.org/10.1515/crelle.2011.018\">10.1515/crelle.2011.018</a>}, number={653}, journal={Journal für die reine und angewandte Mathematik (Crelles Journal)}, publisher={Walter de Gruyter GmbH}, author={Januszewski, Fabian}, year={2010}, pages={1–45} }","ama":"Januszewski F. Modular symbols for reductive groups and p-adic Rankin–Selberg convolutions over number fields. <i>Journal für die reine und angewandte Mathematik (Crelles Journal)</i>. 2010;2011(653):1-45. doi:<a href=\"https://doi.org/10.1515/crelle.2011.018\">10.1515/crelle.2011.018</a>","mla":"Januszewski, Fabian. “Modular Symbols for Reductive Groups and P-Adic Rankin–Selberg Convolutions over Number Fields.” <i>Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)</i>, vol. 2011, no. 653, Walter de Gruyter GmbH, 2010, pp. 1–45, doi:<a href=\"https://doi.org/10.1515/crelle.2011.018\">10.1515/crelle.2011.018</a>.","chicago":"Januszewski, Fabian. “Modular Symbols for Reductive Groups and P-Adic Rankin–Selberg Convolutions over Number Fields.” <i>Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)</i> 2011, no. 653 (2010): 1–45. <a href=\"https://doi.org/10.1515/crelle.2011.018\">https://doi.org/10.1515/crelle.2011.018</a>.","short":"F. Januszewski, Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 2011 (2010) 1–45.","ieee":"F. Januszewski, “Modular symbols for reductive groups and p-adic Rankin–Selberg convolutions over number fields,” <i>Journal für die reine und angewandte Mathematik (Crelles Journal)</i>, vol. 2011, no. 653, pp. 1–45, 2010, doi: <a href=\"https://doi.org/10.1515/crelle.2011.018\">10.1515/crelle.2011.018</a>.","apa":"Januszewski, F. (2010). Modular symbols for reductive groups and p-adic Rankin–Selberg convolutions over number fields. <i>Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)</i>, <i>2011</i>(653), 1–45. <a href=\"https://doi.org/10.1515/crelle.2011.018\">https://doi.org/10.1515/crelle.2011.018</a>"},"page":"1-45","_id":"53184","publisher":"Walter de Gruyter GmbH","user_id":"81636","volume":2011,"status":"public"},{"external_id":{"arxiv":["math/0112318"]},"citation":{"bibtex":"@article{Klüners_Malle_2006, title={Counting nilpotent Galois extensions}, volume={2004}, DOI={<a href=\"https://doi.org/10.1515/crll.2004.050\">10.1515/crll.2004.050</a>}, number={572}, journal={Journal für die reine und angewandte Mathematik (Crelles Journal)}, publisher={Walter de Gruyter GmbH}, author={Klüners, Jürgen and Malle, G.}, year={2006}, pages={1–26} }","ama":"Klüners J, Malle G. Counting nilpotent Galois extensions. <i>Journal für die reine und angewandte Mathematik (Crelles Journal)</i>. 2006;2004(572):1-26. doi:<a href=\"https://doi.org/10.1515/crll.2004.050\">10.1515/crll.2004.050</a>","mla":"Klüners, Jürgen, and G. Malle. “Counting Nilpotent Galois Extensions.” <i>Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)</i>, vol. 2004, no. 572, Walter de Gruyter GmbH, 2006, pp. 1–26, doi:<a href=\"https://doi.org/10.1515/crll.2004.050\">10.1515/crll.2004.050</a>.","chicago":"Klüners, Jürgen, and G. Malle. “Counting Nilpotent Galois Extensions.” <i>Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)</i> 2004, no. 572 (2006): 1–26. <a href=\"https://doi.org/10.1515/crll.2004.050\">https://doi.org/10.1515/crll.2004.050</a>.","short":"J. Klüners, G. Malle, Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 2004 (2006) 1–26.","ieee":"J. Klüners and G. Malle, “Counting nilpotent Galois extensions,” <i>Journal für die reine und angewandte Mathematik (Crelles Journal)</i>, vol. 2004, no. 572, pp. 1–26, 2006, doi: <a href=\"https://doi.org/10.1515/crll.2004.050\">10.1515/crll.2004.050</a>.","apa":"Klüners, J., &#38; Malle, G. (2006). Counting nilpotent Galois extensions. <i>Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)</i>, <i>2004</i>(572), 1–26. <a href=\"https://doi.org/10.1515/crll.2004.050\">https://doi.org/10.1515/crll.2004.050</a>"},"publisher":"Walter de Gruyter GmbH","_id":"34895","page":"1-26","volume":2004,"user_id":"93826","status":"public","date_created":"2022-12-23T09:50:49Z","department":[{"_id":"102"}],"keyword":["Applied Mathematics","General Mathematics"],"type":"journal_article","issue":"572","publication":"Journal für die reine und angewandte Mathematik (Crelles Journal)","abstract":[{"text":"We obtain strong information on the asymptotic behaviour of the counting function for nilpotent Galois extensions with bounded discriminant of arbitrary number fields. This extends previous investigations for the case of abelian groups. In particular, the result confirms a conjecture by the second author on this function for arbitrary groups in the nilpotent case. We further prove compatibility of the conjecture with taking wreath products with the cyclic group of order 2 and give examples in degree up to 8. ","lang":"eng"}],"language":[{"iso":"eng"}],"doi":"10.1515/crll.2004.050","author":[{"last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202"},{"full_name":"Malle, G.","last_name":"Malle","first_name":"G."}],"publication_identifier":{"issn":["0075-4102","1435-5345"]},"title":"Counting nilpotent Galois extensions","year":"2006","intvolume":"      2004","publication_status":"published","date_updated":"2023-03-06T09:11:16Z"}]