Divisibility of class numbers: enumerative approach

Yuri F. Bilu; Florian Luca

Divisibility of class numbers: enumerative approach

Number Theory 2007-05-23 v1

Authors: Yuri F. Bilu , Florian Luca

Abstract

Murty proved that for all sufficiently large $X$ there exist at least ${c(\ell,\eps) X^{1/{4\ell}-\eps}}$ real quadratic fields with class number divisible by $\ell$ and discriminant not exceeding $X$ in absolute value. We extend this this to number fields of arbitrary degree.

Keywords

class number of quadratic fields fields quadratic forms

Cite

@article{arxiv.math/0410246,
  title  = {Divisibility of class numbers: enumerative approach},
  author = {Yuri F. Bilu and Florian Luca},
  journal= {arXiv preprint arXiv:math/0410246},
  year   = {2007}
}

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