IJPAM: Volume 22, No. 2 (2005)

ALGEBRAIC PROOF OF GAUSS
QUADRATIC RECIPROCITY

Marek Szyjewski
Institute of Mathematics
Silesian University
Bankowa 14 Str., Katowice, 40007, POLAND
e-mail: szyjewsk@gate.math.us.edu.pl


Abstract.Zolotareff expression of Legendre symbol by sign of permutation of regular representation of multiplicative group of a finite field applied to the Galois group of an extension of a finite field yields the Quadratic Reciprocity Law.

Received: June 6, 2005

AMS Subject Classification: 11A15, 11T99, 12F10

Key Words and Phrases: Legendre symbol, quadratic reciprocity, permutation, Frobenius automorphism

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 2