Class numbers of ternary quadratic forms

JOURNAL OF NUMBER THEORY

卷:135

Article

Chan, Wai Kiu¹  Oh, Byeong-Kweon^2,3 

[1] Wesleyan Univ, Dept Math & Comp Sci, Middletown, CT 06459 USA

[2] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[3] Seoul Natl Univ, Res Inst Math, Seoul 151747, South Korea

关键词: Class numbers;    Quadratic forms;   

DOI  :  10.1016/j.jnt.2013.08.011

来源: Elsevier

【 摘 要 】

G.L. Watson [13,14] introduced a set of transformations, called Watson transformations by most recent authors, in his study of the arithmetic of integral quadratic forms. These transformations change an integral quadratic form to another integral quadratic form with a smaller discriminant, but preserve many arithmetic properties at the same time. In this paper, we study the change of class numbers of positive definite ternary integral quadratic formula along a sequence of Watson transformations, thus providing a new and effective way to compute the class number of positive definite ternary integral quadratic forms. Explicit class number formulae for many genera of positive definite ternary integral quadratic forms are derived as illustrations of our method. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free