On Dirichlet's conjecture on relative class number one

JOURNAL OF NUMBER THEORY

卷:132

Article

Furness, Amanda¹  Parker, Adam E.¹ 

[1] Wittenberg Univ, Dept Math, Springfield, OH 45501 USA

关键词: Quadratic fields;    Relative class number;    Continued fractions;   

DOI  :  10.1016/j.jnt.2012.01.009

来源: Elsevier

【 摘 要 】

Dirichlet conjectured that for every square-free m > 0, there exists f > 1 such that the relative class number of Q(root f(2)d) is one. where d is the field discriminant of Q(root m). We prove Dirichlet's conjecture is true when root m has a particular continued fraction form. Published by Elsevier Inc.

【 授权许可】

Free