A note on the divisibility of class numbers of real quadratic fields

JOURNAL OF NUMBER THEORY

卷:97

Article

Yu, G

关键词: quadratic fields;    class numbers;    binary forms;   

DOI  :  10.1006/jnth.2001.2773

来源: Elsevier

【 摘 要 】

Suppose g > 2 is an odd integer. For real number X > 2, define S-g(X) the number of squarefree integers dless than or equal toX with the class number of the real quadratic field Q(rootd) being divisible by g. By constructing the discriminants based on the work of Yamamoto, we prove that a lower bound S-g(X) >> (X) over dot (1/9-epsilon) holds for any fixed epsilon > 0, which improves a result of Ram Murty. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free