Arithmetic of Pell surfaces

Details Arithmetic of Pell surfaces Arithmetic of Pell surfaces

2011-08-31

arxiv.org/abs/1108.6305v1

Acta Arith. 146, No. 1, 1-12 (2011)

Mathematics

Number Theory

Scientific paper

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 $n$-torsion subgroup of the narrow ideal class group of the quadratic number field Q(\sqrt{\Delta}).

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