{"doi":"10.1016/j.jnt.2013.10.007","intvolume":"       136","_id":"42793","page":"375-393","type":"journal_article","year":"2014","publication_status":"published","extern":"1","publisher":"Elsevier BV","publication_identifier":{"issn":["0022-314X"]},"abstract":[{"lang":"eng","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."}],"title":"One-class genera of maximal integral quadratic forms","status":"public","date_created":"2023-03-07T08:29:34Z","language":[{"iso":"eng"}],"user_id":"93826","date_updated":"2023-04-04T09:13:29Z","department":[{"_id":"102"}],"publication":"Journal of Number Theory","keyword":["Algebra and Number Theory"],"author":[{"first_name":"Markus","id":"82258","full_name":"Kirschmer, Markus","last_name":"Kirschmer"}],"volume":136,"citation":{"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>.","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>","short":"M. Kirschmer, Journal of Number Theory 136 (2014) 375–393.","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>.","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>.","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} }","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>"}}