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 $7/8-\varepsilon$.
Publié le : 2007-01-15
Classification:
class number,
quadratic field,
divisible,
density,
11R29,
11R11,
11R47
@article{1229618751,
author = {Heath-Brown, D. Rodger},
title = {Quadratic Class Numbers Divisible by 3},
journal = {Funct. Approx. Comment. Math.},
volume = {37},
number = {1},
year = {2007},
pages = { 203-211},
language = {en},
url = {http://dml.mathdoc.fr/item/1229618751}
}
Heath-Brown, D. Rodger. Quadratic Class Numbers Divisible by 3. Funct. Approx. Comment. Math., Tome 37 (2007) no. 1, pp. 203-211. http://gdmltest.u-ga.fr/item/1229618751/