Universal forms over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{Q}(\sqrt{5})$\end{document}

被引:0
作者
Young Min Lee
机构
[1] Pohang University of Science and Technology,Pohang Mathematical Institute
关键词
Quadratic forms; Universal forms; Class number; Mass formula; 11E10; 11E41; 11E25;
D O I
10.1007/s11139-007-9099-4
中图分类号
学科分类号
摘要
In this paper, we find all quaternary universal positive definite integral quadratic forms over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{Q}(\sqrt{5})$\end{document} and prove an analogue of Conway and Schneeberger’s 15-Theorem.
引用
收藏
相关论文
共 26 条
  • [1] Bhargava M.(1999)On the Conway-Schneeberger Fifteen Theorem Contemp. Math. 272 27-37
  • [2] Chan W.K.(1996)Ternary universal integral quadratic forms Jpn. J. Math. 22 263-273
  • [3] Kim M.-H.(1927)Quaternary quadratic forms representing all integers Am. J. Math. 49 39-56
  • [4] Raghavan S.(1978)Representation of positive definite quadratic forms J. Reine Angew. Math. 301 132-141
  • [5] Dickson L.E.(1998)On nonvanishing sum of integral squares of Kanweon-Kyungki Math. J. 6 299-302
  • [6] Hsia J.S.(2004)Recent developments on universal forms Contemp. Math. 344 215-228
  • [7] Kitaoka Y.(1999)2-Universal positive definite integral quinary quadratic forms Contemp. Math. 249 51-62
  • [8] Kneser M.(2005)A finiteness theorem for representability of quadratic forms by forms J. Reine Angew. Math. 581 23-30
  • [9] Kim B.M.(1971)Die Maße der Geschlechter quadratischer Formen vom Range ≤3 in quadratischen Zahlkörpern Math. Ann. 193 279-314
  • [10] Kim M.H.(1973)Bestimmung einklassiger Geschlechter ternärer quadratischer Formen in reell-quadratischen Zahlkörpern Math. Ann. 210 91-95