Titlebook: Reciprocity Laws; From Euler to Eisens Franz Lemmermeyer Book 2000 Springer-Verlag Berlin Heidelberg 2000 Algebra.Elliptic functions.Gaus a

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The Genesis of Quadratic Reciprocity,und very early on (see [Ene]) — in connection with the problem of characterizing perfect squares — the history of modern number theory starts with the editions of the books of Diophantus, in particular with the commented edition by Bachet in 1621.

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Eisenstein Reciprocity,t the unique factorization theorem fails to hold for the rings ℤ[ζ.], was overcome by Kummer through the invention of his ideal numbers. The direct generalization of the proofs for cubic and quartic reciprocity, however, did not yield the general reciprocity theorem for .-th powers: indeed, the most