Odd quadratic orders and real $j$-invariants

Yuri G. Zarhin

Odd quadratic orders and real $j$-invariants

Number Theory 2024-07-30 v2 Algebraic Geometry

Authors: Yuri G. Zarhin

Abstract

Let $O$ be an order of odd discriminant $D$ in an imaginary quadratic field $K$ . Let $Cl(O)$ be the group of proper $O$ -ideals and $Cl(O)[2]$ the kernel of multiplication by $2$ in $Cl(O)$ . We describe explicitly the group $Cl(O)[2]$ . In particular, we prove that its order is $2^{s_D-1}$ where $s_D$ is the number of prime divisors of $D$ .

Keywords

class number of quadratic fields perfect numbers

Cite

@article{arxiv.2407.16703,
  title  = {Odd quadratic orders and real $j$-invariants},
  author = {Yuri G. Zarhin},
  journal= {arXiv preprint arXiv:2407.16703},
  year   = {2024}
}

Comments

The results of the paper were already known. I am grateful to Yuri Bilu for pointing it out

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