Sums of squares and orthogonal integral vectors

JOURNAL OF NUMBER THEORY

卷:132

Article

Goswick, Lee M.¹  Kiss, Emil W.²  Moussong, Gabor³  Simanyi, Nandor¹ 

[1] Univ Alabama, Dept Math, Birmingham, AL 35294 USA

[2] Eotvos Lorand Univ, Dept Algebra & Number Theory, H-1117 Budapest, Hungary

[3] Eotvos Lorand Univ, Dept Geometry, H-1117 Budapest, Hungary

关键词: Cubic lattice;    Euler rotation matrix;    Hurwitz integral quaternion;   

DOI  :  10.1016/j.jnt.2011.07.001

来源: Elsevier

【 摘 要 】

Two vectors in Z(3) are called twins if they are orthogonal and have the same length. The paper describes twin pairs using cubic lattices, and counts the number of twin pairs with a given length. Integers M with the property that each integral vector with length has a twin are called twin-complete. They are completely characterized modulo a famous conjecture in number theory. The main tool is the decomposition theory of Hurwitz integral quaternions. Throughout the paper we made a concerted effort to keep the exposition as elementary as possible. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free