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- Title
Redei reciprocity, governing fields and negative Pell.
- Authors
STEVENHAGEN, PETER
- Abstract
We discuss the origin, an improved definition and the key reciprocity property of the trilinear symbol introduced by Rédei [16] 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 in the recent work of A. Smith [18, 19]. In addition, we explain its impact in the progress towards proving my conjectural density for solvability of the negative Pell equation $x^2-dy^2=-1$.
- Subjects
RECIPROCITY (Psychology); CLASS groups (Mathematics)
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2022, Vol 172, Issue 3, p627
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004121000335