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

[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).

[发布日期] 2002-11-01

[关键词] quadratic fields;class numbers;binary forms