Quadratic fields with cyclic 2-class groups

Carlos Dominguez; Steven J. Miller; Siman Wong

Quadratic fields with cyclic 2-class groups

Number Theory 2012-11-13 v1

Authors: Carlos Dominguez , Steven J. Miller , Siman Wong

Abstract

For any integer $k\ge 1$ , we show that there are infinitely many complex quadratic fields whose 2-class groups are cyclic of order $2^k$ . The proof combines the circle method with an algebraic criterion for a complex quadratic ideal class to be a square.

Keywords

class number of quadratic fields quadratic forms fields

Cite

@article{arxiv.1211.2605,
  title  = {Quadratic fields with cyclic 2-class groups},
  author = {Carlos Dominguez and Steven J. Miller and Siman Wong},
  journal= {arXiv preprint arXiv:1211.2605},
  year   = {2012}
}

Comments

final version, 15 pages, to appear in the Journal of Number Theory

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