[{"publication":"arXiv:2604.02152","citation":{"apa":"Klüners, J., &#38; Müller, R. (2026). Counting Frobenius extensions over local function fields. In <i>arXiv:2604.02152</i>.","mla":"Klüners, Jürgen, and Raphael Müller. “Counting Frobenius Extensions over Local Function Fields.” <i>ArXiv:2604.02152</i>, 2026.","ieee":"J. Klüners and R. Müller, “Counting Frobenius extensions over local function fields,” <i>arXiv:2604.02152</i>. 2026.","ama":"Klüners J, Müller R. Counting Frobenius extensions over local function fields. <i>arXiv:260402152</i>. Published online 2026.","short":"J. Klüners, R. Müller, ArXiv:2604.02152 (2026).","chicago":"Klüners, Jürgen, and Raphael Müller. “Counting Frobenius Extensions over Local Function Fields.” <i>ArXiv:2604.02152</i>, 2026.","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} }"},"abstract":[{"lang":"eng","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."}],"external_id":{"arxiv":["2604.02152"]},"date_created":"2026-04-07T08:13:59Z","type":"preprint","year":"2026","title":"Counting Frobenius extensions over local function fields","status":"public","author":[{"full_name":"Klüners, Jürgen","first_name":"Jürgen","last_name":"Klüners","id":"21202"},{"last_name":"Müller","first_name":"Raphael","full_name":"Müller, Raphael","id":"55246"}],"date_updated":"2026-04-07T08:14:45Z","_id":"65358","language":[{"iso":"eng"}],"user_id":"82981"},{"date_updated":"2024-07-12T08:19:11Z","author":[{"first_name":"Fabian","last_name":"Gundlach","full_name":"Gundlach, Fabian","id":"100450"},{"id":"21202","first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen"}],"status":"public","year":"2024","title":"Symmetries of power-free integers in number fields and their shift  spaces","user_id":"82981","_id":"55192","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We describe the group of $\\mathbb Z$-linear automorphisms of the ring of\r\nintegers of a number field $K$ that preserve the set $V_{K,k}$ of $k$th\r\npower-free integers: every such map is the composition of a field automorphism\r\nand the multiplication by a unit.\r\n  We show that those maps together with translations generate the extended\r\nsymmetry group of the shift space $\\mathbb D_{K,k}$ associated to $V_{K,k}$.\r\nMoreover, we show that no two such dynamical systems $\\mathbb D_{K,k}$ and\r\n$\\mathbb D_{L,l}$ are topologically conjugate and no one is a factor system of\r\nanother.\r\n  We generalize the concept of $k$th power-free integers to sieves and study\r\nthe resulting admissible shift spaces."}],"citation":{"ieee":"F. Gundlach and J. Klüners, “Symmetries of power-free integers in number fields and their shift  spaces,” <i>arXiv:2407.08438</i>. 2024.","apa":"Gundlach, F., &#38; Klüners, J. (2024). Symmetries of power-free integers in number fields and their shift  spaces. In <i>arXiv:2407.08438</i>.","chicago":"Gundlach, Fabian, and Jürgen Klüners. “Symmetries of Power-Free Integers in Number Fields and Their Shift  Spaces.” <i>ArXiv:2407.08438</i>, 2024.","short":"F. Gundlach, J. Klüners, ArXiv:2407.08438 (2024).","mla":"Gundlach, Fabian, and Jürgen Klüners. “Symmetries of Power-Free Integers in Number Fields and Their Shift  Spaces.” <i>ArXiv:2407.08438</i>, 2024.","bibtex":"@article{Gundlach_Klüners_2024, title={Symmetries of power-free integers in number fields and their shift  spaces}, journal={arXiv:2407.08438}, author={Gundlach, Fabian and Klüners, Jürgen}, year={2024} }","ama":"Gundlach F, Klüners J. Symmetries of power-free integers in number fields and their shift  spaces. <i>arXiv:240708438</i>. Published online 2024."},"publication":"arXiv:2407.08438","type":"preprint","date_created":"2024-07-12T08:16:37Z","external_id":{"arxiv":["2407.08438"]}},{"abstract":[{"lang":"eng","text":"We arrange the orders in an algebraic number field in a tree. This tree can\r\nbe used to enumerate all orders of bounded index in the maximal order as well\r\nas the orders over some given order."}],"publication":"arXiv:2411.08568","citation":{"chicago":"Kirschmer, Markus, and Jürgen Klüners. “Enumerating Orders in Number Fields.” <i>ArXiv:2411.08568</i>, 2024.","short":"M. Kirschmer, J. Klüners, ArXiv:2411.08568 (2024).","ieee":"M. Kirschmer and J. Klüners, “Enumerating orders in number fields,” <i>arXiv:2411.08568</i>. 2024.","apa":"Kirschmer, M., &#38; Klüners, J. (2024). Enumerating orders in number fields. In <i>arXiv:2411.08568</i>.","bibtex":"@article{Kirschmer_Klüners_2024, title={Enumerating orders in number fields}, journal={arXiv:2411.08568}, author={Kirschmer, Markus and Klüners, Jürgen}, year={2024} }","ama":"Kirschmer M, Klüners J. Enumerating orders in number fields. <i>arXiv:241108568</i>. Published online 2024.","mla":"Kirschmer, Markus, and Jürgen Klüners. “Enumerating Orders in Number Fields.” <i>ArXiv:2411.08568</i>, 2024."},"type":"preprint","external_id":{"arxiv":["2411.08568"]},"date_created":"2024-11-19T07:49:07Z","date_updated":"2024-11-19T07:49:48Z","year":"2024","title":"Enumerating orders in number fields","status":"public","author":[{"full_name":"Kirschmer, Markus","first_name":"Markus","last_name":"Kirschmer"},{"last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202"}],"user_id":"82981","language":[{"iso":"eng"}],"_id":"57218"}]