Arithmetic of Pell surfaces
Number Theory
2011-09-01 v1
Abstract
We define a group stucture on the primitive integer points (A,B,C) of the algebraic variety Q_0(B,C)=A^n, where Q_0 is the principal binary quadratic form of fundamental discriminant \Delta and n is a fixed integer greater than 1. A surjective homomorphism is given from this group to the -torsion subgroup of the narrow ideal class group of the quadratic number field Q(\sqrt{\Delta}).
Keywords
Cite
@article{arxiv.1108.6305,
title = {Arithmetic of Pell surfaces},
author = {Samuel Hambleton and Franz Lemmermeyer},
journal= {arXiv preprint arXiv:1108.6305},
year = {2011}
}