Redei reciprocity, governing fields, and negative Pell
Number Theory
2021-04-13 v3
Abstract
We discuss the origin, an improved definition and the key reciprocity property of the trilinear symbol introduced by R\'edei in the study of 8-ranks of narrow class groups of quadratic number fields. It can be used to show that such 8-ranks are governed by Frobenius conditions on the primes dividing the discriminant, a fact used the recent work of A. Smith. In addition, we explain its impact in the progress towards proving my conjectural density for solvability of the negative Pell equation.
Cite
@article{arxiv.1806.06250,
title = {Redei reciprocity, governing fields, and negative Pell},
author = {Peter Stevenhagen},
journal= {arXiv preprint arXiv:1806.06250},
year = {2021}
}
Comments
27 pages