Eisenstein and the Jacobian varieties of Fermat curves
type: Item
instance of: scholarly article
title: Eisenstein and the Jacobian varieties of Fermat curves
zbMATH Open document ID: 0934.11002
author: Allan Adler
published in: Rocky Mountain Journal of Mathematics
publication date: 1999-04-07T00:00:00Z
full work available at URL: CONT27-1.html
review text: Deep examinations of Gauß' first paper on biquadratic residues (Gauß-Werke II, 65-92) and of parts of Eisenstein's papers ``Zur Theorie der quadratischen Zerfällung der Primzahlen \(8n+3\), \(7n+2\), \(7n+4\)'', ``Beiträge zur Theorie der elliptischen Functionen'', ``Über die Irreductibilität und andere Eigenschaften der Gleichung, von welcher die Theilung der ganzen Lemniscate abhängt'' [Eisenstein, Math. Werke II, 506-535, I, 299-478, II, 536-619] and making use of numerous other papers (of Jacobi, Kronecker, Abel for instance) the author gains new insight that Eisenstein had some way of knowing that certain differentials on the Fermat curve of degree 7 are reducible to elliptic integrals without explicitly transforming them.
reviewed by: Herbert Pieper
Mathematics Subject Classification ID: 11-03
Mathematics Subject Classification ID: 14-03
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 11G30
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 14K20
zbMATH DE Number: 1051524
MaRDI profile type: Publication
OpenAlex ID: W1975519743
cites work: Some integral representations of \(\text{PSL}_2(\mathbb F_p)\) and their applications
cites work: Q3254300
cites work: Modular functions of one variable. IV. Proceedings of the international summer school, University of Antwerp, RUCA, July 17 -- August 3, 1972
cites work: The Klein group in three dimensions
cites work: Q4040824
cites work: On the periods of certain rational integrals. I, II
cites work: Some results on the Mordell-Weil group of the Jacobian of the Fermat curve
cites work: Simple Factors in the Jacobian of a Fermat Curve
cites work: Certain Classical Congruences Via Elliptic Curves
cites work: Q3858228
cites work: Q4079943
cites work: A theorem of Brewer on character sums
DOI: 10.1216/RMJM/1181071949
description: scientific article; zbMATH DE number 1051524