Open Access
January 2007 Quadratic Class Numbers Divisible by 3
D. Rodger Heath-Brown
Funct. Approx. Comment. Math. 37(1): 203-211 (January 2007). DOI: 10.7169/facm/1229618751


Let $N_+(X)$ denote the number of distinct real quadratic fields $\mathbb{Q}(\sqrt{d})$ with $d\leq X$ for which $3|h(\mathbb{Q}(\sqrt{d}))$. Define $N_-(X)$ similarly for $\mathbb{Q}(\sqrt{-d})$. It is shown that $N_+(X), N_-(X)\gg X^{9/10-\varepsilon}$ for any $\varepsilon>0$. This improves results of Byeon and Koh [2] and of Soundararajan [7], which had exponent $7/8-\varepsilon$.


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D. Rodger Heath-Brown. "Quadratic Class Numbers Divisible by 3." Funct. Approx. Comment. Math. 37 (1) 203 - 211, January 2007.


Published: January 2007
First available in Project Euclid: 18 December 2008

zbMATH: 1140.11050
MathSciNet: MR2357319
Digital Object Identifier: 10.7169/facm/1229618751

Primary: 11R29
Secondary: 11R11 , 11R47

Keywords: Class number , Density , divisible , quadratic field

Rights: Copyright © 2007 Adam Mickiewicz University

Vol.37 • No. 1 • January 2007
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