Proofs Based on the Theory of Quadratic Forms

Oswald Baumgart

Chapter Chapter 13 in The Quadratic Reciprocity Law, 2015, pp 125-126 from Springer

Abstract: Abstract 1. The main idea in Gauss’s Gauss proof is, as Kummer Kummer observes, the fact that the number of actually existent genera is at most half the number of all possible genera. Gauss has shown that, if the reciprocity law was false, the number of actually existing genera had to be bigger than half the number of all possible genera. – Gauss distinguishes four different cases in his proof, which, as Dirichlet Dirichlet [12] has shown, can be reduced to two by choosing a suitable notation. Here too we have followed Dirichlet’s presentation.

Keywords: Quadratic Form; Gauss's Proof; General Existence; Suitable Notation; Dirichlet (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-16283-6_13

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