Harbingers of Artin's Reciprocity Law. I. The Continuing Story of Auxiliary Primes

2011/09/06 by Lemmermeyer, Franz
#11A15 #11R37 #FOS: Mathematics #History and Overview (math.HO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1109.1228

Abstract

In this article we present the history of auxiliary primes used in proofs of reciprocity laws from the quadratic to Artin's reciprocity law. We also show that the gap in Legendre's proof can be closed with a simple application of Gauss's genus theory.

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