[{"citation":{"apa":"Klüners, J., &#38; Müller, R. (2020). The conductor density of local function fields with abelian Galois group. <i>Journal of Number Theory</i>, <i>212</i>, 311–322. <a href=\"https://doi.org/10.1016/j.jnt.2019.11.007\">https://doi.org/10.1016/j.jnt.2019.11.007</a>","short":"J. Klüners, R. Müller, Journal of Number Theory 212 (2020) 311–322.","bibtex":"@article{Klüners_Müller_2020, title={The conductor density of local function fields with abelian Galois group}, volume={212}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2019.11.007\">10.1016/j.jnt.2019.11.007</a>}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Klüners, Jürgen and Müller, Raphael}, year={2020}, pages={311–322} }","mla":"Klüners, Jürgen, and Raphael Müller. “The Conductor Density of Local Function Fields with Abelian Galois Group.” <i>Journal of Number Theory</i>, vol. 212, Elsevier BV, 2020, pp. 311–22, doi:<a href=\"https://doi.org/10.1016/j.jnt.2019.11.007\">10.1016/j.jnt.2019.11.007</a>.","ieee":"J. Klüners and R. Müller, “The conductor density of local function fields with abelian Galois group,” <i>Journal of Number Theory</i>, vol. 212, pp. 311–322, 2020, doi: <a href=\"https://doi.org/10.1016/j.jnt.2019.11.007\">10.1016/j.jnt.2019.11.007</a>.","chicago":"Klüners, Jürgen, and Raphael Müller. “The Conductor Density of Local Function Fields with Abelian Galois Group.” <i>Journal of Number Theory</i> 212 (2020): 311–22. <a href=\"https://doi.org/10.1016/j.jnt.2019.11.007\">https://doi.org/10.1016/j.jnt.2019.11.007</a>.","ama":"Klüners J, Müller R. The conductor density of local function fields with abelian Galois group. <i>Journal of Number Theory</i>. 2020;212:311-322. doi:<a href=\"https://doi.org/10.1016/j.jnt.2019.11.007\">10.1016/j.jnt.2019.11.007</a>"},"intvolume":"       212","page":"311-322","publication_status":"published","publication_identifier":{"issn":["0022-314X"]},"doi":"10.1016/j.jnt.2019.11.007","author":[{"last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202","first_name":"Jürgen"},{"last_name":"Müller","full_name":"Müller, Raphael","first_name":"Raphael"}],"volume":212,"date_updated":"2025-06-13T08:18:30Z","status":"public","type":"journal_article","user_id":"82981","department":[{"_id":"102"}],"_id":"34841","year":"2020","title":"The conductor density of local function fields with abelian Galois group","date_created":"2022-12-22T10:50:03Z","publisher":"Elsevier BV","abstract":[{"text":"We give an exact formula for the number of G-extensions of local function fields Fq((t)) for finite abelian groups G up to a conductor bound. As an application we give a lower bound for the corresponding counting problem by discriminant.\r\n","lang":"eng"}],"publication":"Journal of Number Theory","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"external_id":{"arxiv":["1904.02573 "]}},{"keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"_id":"34916","user_id":"82258","department":[{"_id":"102"}],"abstract":[{"text":"We describe the powers of irreducible polynomials occurring as characteristic polynomials of automorphisms of even unimodular lattices over number fields. This generalizes results of Gross & McMullen and Bayer-Fluckiger & Taelman.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Journal of Number Theory","title":"Automorphisms of even unimodular lattices over number fields","doi":"10.1016/j.jnt.2018.08.004","publisher":"Elsevier BV","date_updated":"2023-12-06T10:07:17Z","author":[{"first_name":"Markus","id":"82258","full_name":"Kirschmer, Markus","last_name":"Kirschmer"}],"date_created":"2022-12-23T11:04:34Z","volume":197,"year":"2019","citation":{"apa":"Kirschmer, M. (2019). Automorphisms of even unimodular lattices over number fields. <i>Journal of Number Theory</i>, <i>197</i>, 121–134. <a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">https://doi.org/10.1016/j.jnt.2018.08.004</a>","mla":"Kirschmer, Markus. “Automorphisms of Even Unimodular Lattices over Number Fields.” <i>Journal of Number Theory</i>, vol. 197, Elsevier BV, 2019, pp. 121–34, doi:<a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">10.1016/j.jnt.2018.08.004</a>.","bibtex":"@article{Kirschmer_2019, title={Automorphisms of even unimodular lattices over number fields}, volume={197}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">10.1016/j.jnt.2018.08.004</a>}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer, Markus}, year={2019}, pages={121–134} }","short":"M. Kirschmer, Journal of Number Theory 197 (2019) 121–134.","ama":"Kirschmer M. Automorphisms of even unimodular lattices over number fields. <i>Journal of Number Theory</i>. 2019;197:121-134. doi:<a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">10.1016/j.jnt.2018.08.004</a>","ieee":"M. Kirschmer, “Automorphisms of even unimodular lattices over number fields,” <i>Journal of Number Theory</i>, vol. 197, pp. 121–134, 2019, doi: <a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">10.1016/j.jnt.2018.08.004</a>.","chicago":"Kirschmer, Markus. “Automorphisms of Even Unimodular Lattices over Number Fields.” <i>Journal of Number Theory</i> 197 (2019): 121–34. <a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">https://doi.org/10.1016/j.jnt.2018.08.004</a>."},"page":"121-134","intvolume":"       197","publication_status":"published","publication_identifier":{"issn":["0022-314X"]}},{"year":"2016","date_created":"2022-12-22T10:52:47Z","publisher":"Elsevier BV","title":"Are number fields determined by Artin L-functions?","publication":"Journal of Number Theory","abstract":[{"lang":"eng","text":"Let k be a number field, K/k a finite Galois extension with Galois group G, χ a faithful character of G. We prove that the Artin L-function L(s,χ,K/k) determines the Galois closure of K over $\\ℚ$. In the special case $k=\\ℚ$ it also determines the character χ. "}],"external_id":{"arxiv":["1509.06883 "]},"language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"publication_identifier":{"issn":["0022-314X"]},"publication_status":"published","intvolume":"       167","page":"161-168","citation":{"ieee":"J. Klüners and F. Nicolae, “Are number fields determined by Artin L-functions?,” <i>Journal of Number Theory</i>, vol. 167, pp. 161–168, 2016, doi: <a href=\"https://doi.org/10.1016/j.jnt.2016.03.023\">10.1016/j.jnt.2016.03.023</a>.","chicago":"Klüners, Jürgen, and Florin Nicolae. “Are Number Fields Determined by Artin L-Functions?” <i>Journal of Number Theory</i> 167 (2016): 161–68. <a href=\"https://doi.org/10.1016/j.jnt.2016.03.023\">https://doi.org/10.1016/j.jnt.2016.03.023</a>.","ama":"Klüners J, Nicolae F. Are number fields determined by Artin L-functions? <i>Journal of Number Theory</i>. 2016;167:161-168. doi:<a href=\"https://doi.org/10.1016/j.jnt.2016.03.023\">10.1016/j.jnt.2016.03.023</a>","apa":"Klüners, J., &#38; Nicolae, F. (2016). Are number fields determined by Artin L-functions? <i>Journal of Number Theory</i>, <i>167</i>, 161–168. <a href=\"https://doi.org/10.1016/j.jnt.2016.03.023\">https://doi.org/10.1016/j.jnt.2016.03.023</a>","short":"J. Klüners, F. Nicolae, Journal of Number Theory 167 (2016) 161–168.","bibtex":"@article{Klüners_Nicolae_2016, title={Are number fields determined by Artin L-functions?}, volume={167}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2016.03.023\">10.1016/j.jnt.2016.03.023</a>}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Klüners, Jürgen and Nicolae, Florin}, year={2016}, pages={161–168} }","mla":"Klüners, Jürgen, and Florin Nicolae. “Are Number Fields Determined by Artin L-Functions?” <i>Journal of Number Theory</i>, vol. 167, Elsevier BV, 2016, pp. 161–68, doi:<a href=\"https://doi.org/10.1016/j.jnt.2016.03.023\">10.1016/j.jnt.2016.03.023</a>."},"volume":167,"author":[{"id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen"},{"first_name":"Florin","full_name":"Nicolae, Florin","last_name":"Nicolae"}],"date_updated":"2023-03-06T10:44:22Z","doi":"10.1016/j.jnt.2016.03.023","type":"journal_article","status":"public","department":[{"_id":"102"}],"user_id":"93826","_id":"34844"},{"title":"Ternary quadratic forms over number fields with small class number","date_created":"2023-03-07T08:28:46Z","publisher":"Elsevier BV","year":"2016","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"abstract":[{"text":"We enumerate all positive definite ternary quadratic forms over number fields with class number at most 2. This is done by constructing all definite quaternion orders of type number at most 2 over number fields. Finally, we list all definite quaternion orders of ideal class number 1 or 2.","lang":"eng"}],"publication":"Journal of Number Theory","doi":"10.1016/j.jnt.2014.11.001","author":[{"first_name":"Markus","last_name":"Kirschmer","full_name":"Kirschmer, Markus","id":"82258"},{"first_name":"David","last_name":"Lorch","full_name":"Lorch, David"}],"volume":161,"date_updated":"2023-04-04T09:10:42Z","citation":{"ama":"Kirschmer M, Lorch D. Ternary quadratic forms over number fields with small class number. <i>Journal of Number Theory</i>. 2016;161:343-361. doi:<a href=\"https://doi.org/10.1016/j.jnt.2014.11.001\">10.1016/j.jnt.2014.11.001</a>","chicago":"Kirschmer, Markus, and David Lorch. “Ternary Quadratic Forms over Number Fields with Small Class Number.” <i>Journal of Number Theory</i> 161 (2016): 343–61. <a href=\"https://doi.org/10.1016/j.jnt.2014.11.001\">https://doi.org/10.1016/j.jnt.2014.11.001</a>.","ieee":"M. Kirschmer and D. Lorch, “Ternary quadratic forms over number fields with small class number,” <i>Journal of Number Theory</i>, vol. 161, pp. 343–361, 2016, doi: <a href=\"https://doi.org/10.1016/j.jnt.2014.11.001\">10.1016/j.jnt.2014.11.001</a>.","apa":"Kirschmer, M., &#38; Lorch, D. (2016). Ternary quadratic forms over number fields with small class number. <i>Journal of Number Theory</i>, <i>161</i>, 343–361. <a href=\"https://doi.org/10.1016/j.jnt.2014.11.001\">https://doi.org/10.1016/j.jnt.2014.11.001</a>","bibtex":"@article{Kirschmer_Lorch_2016, title={Ternary quadratic forms over number fields with small class number}, volume={161}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2014.11.001\">10.1016/j.jnt.2014.11.001</a>}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer, Markus and Lorch, David}, year={2016}, pages={343–361} }","mla":"Kirschmer, Markus, and David Lorch. “Ternary Quadratic Forms over Number Fields with Small Class Number.” <i>Journal of Number Theory</i>, vol. 161, Elsevier BV, 2016, pp. 343–61, doi:<a href=\"https://doi.org/10.1016/j.jnt.2014.11.001\">10.1016/j.jnt.2014.11.001</a>.","short":"M. Kirschmer, D. Lorch, Journal of Number Theory 161 (2016) 343–361."},"intvolume":"       161","page":"343-361","publication_status":"published","publication_identifier":{"issn":["0022-314X"]},"extern":"1","user_id":"93826","department":[{"_id":"102"}],"_id":"42792","status":"public","type":"journal_article"},{"abstract":[{"text":"Suppose Q is a definite quadratic form on a vector space V over some totally real field K ≠ Q. Then the maximal integral Zₖ-lattices in (V,Q) are locally isometric everywhere and hence form a single genus. We enumerate all orthogonal spaces (V,Q) of dimension at least 3, where the corresponding genus of maximal integral lattices consists of a single isometry class. It turns out, there are 471 such genera. Moreover, the dimension of V and the degree of K are bounded by 6 and 5 respectively. This classification also yields all maximal quaternion orders of type number one.","lang":"eng"}],"publication":"Journal of Number Theory","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"year":"2014","title":"One-class genera of maximal integral quadratic forms","publisher":"Elsevier BV","date_created":"2023-03-07T08:29:34Z","status":"public","type":"journal_article","extern":"1","_id":"42793","department":[{"_id":"102"}],"user_id":"93826","intvolume":"       136","page":"375-393","citation":{"bibtex":"@article{Kirschmer_2014, title={One-class genera of maximal integral quadratic forms}, volume={136}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2013.10.007\">10.1016/j.jnt.2013.10.007</a>}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer, Markus}, year={2014}, pages={375–393} }","mla":"Kirschmer, Markus. “One-Class Genera of Maximal Integral Quadratic Forms.” <i>Journal of Number Theory</i>, vol. 136, Elsevier BV, 2014, pp. 375–93, doi:<a href=\"https://doi.org/10.1016/j.jnt.2013.10.007\">10.1016/j.jnt.2013.10.007</a>.","short":"M. Kirschmer, Journal of Number Theory 136 (2014) 375–393.","apa":"Kirschmer, M. (2014). One-class genera of maximal integral quadratic forms. <i>Journal of Number Theory</i>, <i>136</i>, 375–393. <a href=\"https://doi.org/10.1016/j.jnt.2013.10.007\">https://doi.org/10.1016/j.jnt.2013.10.007</a>","ieee":"M. Kirschmer, “One-class genera of maximal integral quadratic forms,” <i>Journal of Number Theory</i>, vol. 136, pp. 375–393, 2014, doi: <a href=\"https://doi.org/10.1016/j.jnt.2013.10.007\">10.1016/j.jnt.2013.10.007</a>.","chicago":"Kirschmer, Markus. “One-Class Genera of Maximal Integral Quadratic Forms.” <i>Journal of Number Theory</i> 136 (2014): 375–93. <a href=\"https://doi.org/10.1016/j.jnt.2013.10.007\">https://doi.org/10.1016/j.jnt.2013.10.007</a>.","ama":"Kirschmer M. One-class genera of maximal integral quadratic forms. <i>Journal of Number Theory</i>. 2014;136:375-393. doi:<a href=\"https://doi.org/10.1016/j.jnt.2013.10.007\">10.1016/j.jnt.2013.10.007</a>"},"publication_identifier":{"issn":["0022-314X"]},"publication_status":"published","doi":"10.1016/j.jnt.2013.10.007","date_updated":"2023-04-04T09:13:29Z","volume":136,"author":[{"first_name":"Markus","last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus"}]},{"publication":"Journal of Number Theory","abstract":[{"text":"We apply class field theory to the computation of the minimal discriminants for certain solvable groups. In particular, we apply our techniques to small Frobenius groups and all imprimitive degree 8 groups such that the corresponding fields have only a degree 2 and no degree 4 subfield.","lang":"eng"}],"language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"issue":"2","year":"2003","date_created":"2022-12-23T09:53:23Z","publisher":"Elsevier BV","title":"Minimal discriminants for fields with small Frobenius groups as Galois groups","type":"journal_article","status":"public","department":[{"_id":"102"}],"user_id":"93826","_id":"34896","publication_identifier":{"issn":["0022-314X"]},"publication_status":"published","page":"318-337","intvolume":"        99","citation":{"chicago":"Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with Small Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i> 99, no. 2 (2003): 318–37. <a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">https://doi.org/10.1016/s0022-314x(02)00071-9</a>.","ieee":"C. Fieker and J. Klüners, “Minimal discriminants for fields with small Frobenius groups as Galois groups,” <i>Journal of Number Theory</i>, vol. 99, no. 2, pp. 318–337, 2003, doi: <a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>.","ama":"Fieker C, Klüners J. Minimal discriminants for fields with small Frobenius groups as Galois groups. <i>Journal of Number Theory</i>. 2003;99(2):318-337. doi:<a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>","short":"C. Fieker, J. Klüners, Journal of Number Theory 99 (2003) 318–337.","bibtex":"@article{Fieker_Klüners_2003, title={Minimal discriminants for fields with small Frobenius groups as Galois groups}, volume={99}, DOI={<a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>}, number={2}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Fieker, Claus and Klüners, Jürgen}, year={2003}, pages={318–337} }","mla":"Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with Small Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i>, vol. 99, no. 2, Elsevier BV, 2003, pp. 318–37, doi:<a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>.","apa":"Fieker, C., &#38; Klüners, J. (2003). Minimal discriminants for fields with small Frobenius groups as Galois groups. <i>Journal of Number Theory</i>, <i>99</i>(2), 318–337. <a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">https://doi.org/10.1016/s0022-314x(02)00071-9</a>"},"volume":99,"author":[{"first_name":"Claus","last_name":"Fieker","full_name":"Fieker, Claus"},{"first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners"}],"date_updated":"2023-03-06T09:19:16Z","doi":"10.1016/s0022-314x(02)00071-9"}]