The Fourier-analytic proof of quadratic reciprocity

Description:

"The relative quadratic case was first settled by Hecke in 1923, then recast by Weil in 1964 into the language of unitary group representations. The analytic proof of the general n-th order case is still an open problem today, going back to the end of Heckes famous treatise of 1923. The Fourier-Analytic Proof of Quadratic Reciprocity provides number theorists interested in analytic methods applied to reciprocity laws with a unique opportunity to explore the works of Hecke, Weil, and Kubota.". "This work brings together for the first time in a single volume the three existing formulations of the Fourier-analytic proof of quadratic reciprocity. It shows how Weil's ground-breaking representation-theoretic treatment is in fact equivalent to Hecke's classical approach, then goes a step further, presenting Kubota's algebraic reformulation of the Hecke-Weil proof. Extensive commutative diagrams for comparing the Weil and Kubota architectures are also featured."--BOOK JACKET.

subjects: Reciprocity theorems,  Equations, quartic,  Fourier analysis