Redei reciprocity, governing fields, and negative Pell

Autor:	Stevenhagen, Peter
Rok vydání:	2018
Předmět:	Mathematics - Number Theory Primary 11R11 11R37 Secondary 11R16
Zdroj:	Math. Proc. of the Cambridge Phil. Soc., 2021
Druh dokumentu:	Working Paper
Popis:	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. Comment: 27 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1806.06250 Zobrazit plný text záznamu View this record from Arxiv