[{"date_updated":"2026-04-07T08:14:45Z","year":"2026","title":"Counting Frobenius extensions over local function fields","status":"public","author":[{"id":"21202","first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen"},{"id":"55246","full_name":"Müller, Raphael","last_name":"Müller","first_name":"Raphael"}],"user_id":"82981","language":[{"iso":"eng"}],"_id":"65358","abstract":[{"text":"We determine the asymptotic growth of extensions of local function fields of characteristic p counted by discriminant, where the Galois group is a subgroup of the affine group AGL_1(p). More general, we solve the corresponding counting problems for all groups which arise in a tower of a cyclic extension of order p over a cyclic extension of degree d coprime to p. This in particular give answers for certain non-abelian groups including S_3, dihedral groups of order 2p, and many Frobenius groups.","lang":"eng"}],"publication":"arXiv:2604.02152","citation":{"bibtex":"@article{Klüners_Müller_2026, title={Counting Frobenius extensions over local function fields}, journal={arXiv:2604.02152}, author={Klüners, Jürgen and Müller, Raphael}, year={2026} }","chicago":"Klüners, Jürgen, and Raphael Müller. “Counting Frobenius Extensions over Local Function Fields.” <i>ArXiv:2604.02152</i>, 2026.","short":"J. Klüners, R. Müller, ArXiv:2604.02152 (2026).","ama":"Klüners J, Müller R. Counting Frobenius extensions over local function fields. <i>arXiv:260402152</i>. Published online 2026.","ieee":"J. Klüners and R. Müller, “Counting Frobenius extensions over local function fields,” <i>arXiv:2604.02152</i>. 2026.","mla":"Klüners, Jürgen, and Raphael Müller. “Counting Frobenius Extensions over Local Function Fields.” <i>ArXiv:2604.02152</i>, 2026.","apa":"Klüners, J., &#38; Müller, R. (2026). Counting Frobenius extensions over local function fields. In <i>arXiv:2604.02152</i>."},"type":"preprint","external_id":{"arxiv":["2604.02152"]},"date_created":"2026-04-07T08:13:59Z"},{"publication":"INDRUM2024 PROCEEDINGS Fifth conference of the International Network for Didactic Research in University Mathematics","file":[{"relation":"main_file","date_updated":"2025-05-19T08:51:19Z","file_name":"Poster_Indrum_2024_Digital-STACK-Tasks_Exam-Results.pdf","file_size":850253,"access_level":"open_access","file_id":"59991","content_type":"application/pdf","creator":"rmuelle2","date_created":"2025-05-19T08:51:19Z"}],"date_created":"2025-05-19T08:51:27Z","type":"conference","title":"Digital STACK tasks and exam results","year":"2024","author":[{"first_name":"Andreas","last_name":"Eichler","full_name":"Eichler, Andreas"},{"full_name":"Floren, Henrik","first_name":"Henrik","last_name":"Floren"},{"id":"93843","first_name":"Irene","last_name":"Garnelo Abellanas","full_name":"Garnelo Abellanas, Irene"},{"full_name":"Liebendörfer, Michael","orcid":"0000-0001-9887-2074","first_name":"Michael","last_name":"Liebendörfer","id":"30933"},{"full_name":"Müller, Raphael","last_name":"Müller","first_name":"Raphael","id":"55246"},{"full_name":"Schürmann, Mirko","orcid":"0000-0003-2646-085X","first_name":"Mirko","last_name":"Schürmann","id":"59707"},{"last_name":"Speer","first_name":"Annabelle","full_name":"Speer, Annabelle"}],"publication_identifier":{"issn":["2496-1027 (online)"]},"date_updated":"2025-06-25T07:50:49Z","publication_status":"published","main_file_link":[{"url":"https://theses.hal.science/INDRUM2024/hal-04944194v1"}],"language":[{"iso":"eng"}],"doi":"https://theses.hal.science/INDRUM2024/hal-04944194v1","file_date_updated":"2025-05-19T08:51:19Z","citation":{"ama":"Eichler A, Floren H, Garnelo Abellanas I, et al. Digital STACK tasks and exam results. In: <i>INDRUM2024 PROCEEDINGS Fifth Conference of the International Network for Didactic Research in University Mathematics</i>. Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM; 2024. doi:<a href=\"https://theses.hal.science/INDRUM2024/hal-04944194v1\">https://theses.hal.science/INDRUM2024/hal-04944194v1</a>","bibtex":"@inproceedings{Eichler_Floren_Garnelo Abellanas_Liebendörfer_Müller_Schürmann_Speer_2024, place={Barcelona}, title={Digital STACK tasks and exam results}, DOI={<a href=\"https://theses.hal.science/INDRUM2024/hal-04944194v1\">https://theses.hal.science/INDRUM2024/hal-04944194v1</a>}, booktitle={INDRUM2024 PROCEEDINGS Fifth conference of the International Network for Didactic Research in University Mathematics}, publisher={Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM}, author={Eichler, Andreas and Floren, Henrik and Garnelo Abellanas, Irene and Liebendörfer, Michael and Müller, Raphael and Schürmann, Mirko and Speer, Annabelle}, year={2024} }","mla":"Eichler, Andreas, et al. “Digital STACK Tasks and Exam Results.” <i>INDRUM2024 PROCEEDINGS Fifth Conference of the International Network for Didactic Research in University Mathematics</i>, Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM, 2024, doi:<a href=\"https://theses.hal.science/INDRUM2024/hal-04944194v1\">https://theses.hal.science/INDRUM2024/hal-04944194v1</a>.","chicago":"Eichler, Andreas, Henrik Floren, Irene Garnelo Abellanas, Michael Liebendörfer, Raphael Müller, Mirko Schürmann, and Annabelle Speer. “Digital STACK Tasks and Exam Results.” In <i>INDRUM2024 PROCEEDINGS Fifth Conference of the International Network for Didactic Research in University Mathematics</i>. Barcelona: Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM, 2024. <a href=\"https://theses.hal.science/INDRUM2024/hal-04944194v1\">https://theses.hal.science/INDRUM2024/hal-04944194v1</a>.","short":"A. Eichler, H. Floren, I. Garnelo Abellanas, M. Liebendörfer, R. Müller, M. Schürmann, A. Speer, in: INDRUM2024 PROCEEDINGS Fifth Conference of the International Network for Didactic Research in University Mathematics, Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM, Barcelona, 2024.","apa":"Eichler, A., Floren, H., Garnelo Abellanas, I., Liebendörfer, M., Müller, R., Schürmann, M., &#38; Speer, A. (2024). Digital STACK tasks and exam results. <i>INDRUM2024 PROCEEDINGS Fifth Conference of the International Network for Didactic Research in University Mathematics</i>. Fifth conference of the International Network for Didactic Research in University Mathematics, Barcelona. <a href=\"https://theses.hal.science/INDRUM2024/hal-04944194v1\">https://theses.hal.science/INDRUM2024/hal-04944194v1</a>","ieee":"A. Eichler <i>et al.</i>, “Digital STACK tasks and exam results,” presented at the Fifth conference of the International Network for Didactic Research in University Mathematics, Barcelona, 2024, doi: <a href=\"https://theses.hal.science/INDRUM2024/hal-04944194v1\">https://theses.hal.science/INDRUM2024/hal-04944194v1</a>."},"place":"Barcelona","oa":"1","status":"public","conference":{"end_date":"2024-06-14","location":"Barcelona","name":"Fifth conference of the International Network for Didactic Research in University Mathematics","start_date":"2024-06-10"},"has_accepted_license":"1","_id":"59990","publisher":"Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM","ddc":["510"],"user_id":"55246"},{"citation":{"mla":"Müller, Raphael. <i>On the Asymptotics of Wildly Ramified Local Function Field Extensions</i>. 2023.","bibtex":"@book{Müller_2023, title={On the asymptotics of wildly ramified local function field extensions}, author={Müller, Raphael}, year={2023} }","ama":"Müller R. <i>On the Asymptotics of Wildly Ramified Local Function Field Extensions</i>.; 2023.","ieee":"R. Müller, <i>On the asymptotics of wildly ramified local function field extensions</i>. 2023.","apa":"Müller, R. (2023). <i>On the asymptotics of wildly ramified local function field extensions</i>.","chicago":"Müller, Raphael. <i>On the Asymptotics of Wildly Ramified Local Function Field Extensions</i>, 2023.","short":"R. Müller, On the Asymptotics of Wildly Ramified Local Function Field Extensions, 2023."},"date_created":"2025-05-19T08:22:06Z","department":[{"_id":"43"}],"oa":"1","type":"dissertation","author":[{"id":"55246","first_name":"Raphael","last_name":"Müller","full_name":"Müller, Raphael"}],"title":"On the asymptotics of wildly ramified local function field extensions","status":"public","year":"2023","publication_status":"published","date_updated":"2025-05-19T08:58:21Z","_id":"59988","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://katalog.ub.uni-paderborn.de/local/r/99372717691706441","open_access":"1"}],"user_id":"55246"},{"user_id":"82981","volume":212,"language":[{"iso":"eng"}],"_id":"59989","date_updated":"2025-06-13T08:15:14Z","intvolume":"       212","status":"public","title":"The conductor density of local function fields with abelian Galois group","year":"2020","author":[{"id":"55246","first_name":"Raphael","last_name":"Müller","full_name":"Müller, Raphael"},{"last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen"}],"type":"journal_article","department":[{"_id":"43"}],"date_created":"2025-05-19T08:31:53Z","related_material":{"link":[{"url":"https://arxiv.org/abs/1904.02573","relation":"earlier_version"}]},"publication":"Journal of Number Theory","citation":{"ama":"Müller R, Klüners J. The conductor density of local function fields with abelian Galois group. <i>Journal of Number Theory</i>. 2020;212.","bibtex":"@article{Müller_Klüners_2020, title={The conductor density of local function fields with abelian Galois group}, volume={212}, journal={Journal of Number Theory}, author={Müller, Raphael and Klüners, Jürgen}, year={2020} }","mla":"Müller, Raphael, and Jürgen Klüners. “The Conductor Density of Local Function Fields with Abelian Galois Group.” <i>Journal of Number Theory</i>, vol. 212, 2020.","chicago":"Müller, Raphael, and Jürgen Klüners. “The Conductor Density of Local Function Fields with Abelian Galois Group.” <i>Journal of Number Theory</i> 212 (2020).","short":"R. Müller, J. Klüners, Journal of Number Theory 212 (2020).","apa":"Müller, R., &#38; Klüners, J. (2020). The conductor density of local function fields with abelian Galois group. <i>Journal of Number Theory</i>, <i>212</i>.","ieee":"R. Müller and J. Klüners, “The conductor density of local function fields with abelian Galois group,” <i>Journal of Number Theory</i>, vol. 212, 2020."}}]