English

Small class number fields in the family $\mathbb{Q}(\sqrt{9m^2+4m})$

Number Theory 2023-05-15 v1

Abstract

We study the class number one problem for real quadratic fields Q(9m2+4m)\mathbb{Q}(\sqrt{9m^2+ 4m}), where mm is an odd integer. We show that for m1(mod3)m \equiv 1 \pmod 3 there is only one such field with class number one and only one such field with class number two.

Keywords

Cite

@article{arxiv.2005.12646,
  title  = {Small class number fields in the family $\mathbb{Q}(\sqrt{9m^2+4m})$},
  author = {Nimish Mahapatra and Prem Prakash Pandey and Mahesh Ram},
  journal= {arXiv preprint arXiv:2005.12646},
  year   = {2023}
}

Comments

20 pages. Comments are welcome