Eisenstein and the Jacobian varieties of Fermat curves
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.
scientific article; zbMATH DE number 1051524
scientific article