Eight lectures on quadratic reciprocity

TL;DR

This paper presents Rousseau's simple proof of quadratic reciprocity, explores its equivalence with Hilbert's product formula, and explains the Hilbert symbol in relation to the reciprocity isomorphism and places of Q.

Contribution

It provides a clear exposition of Rousseau's proof, links it to Hilbert's product formula, and clarifies the role of the Hilbert symbol in quadratic reciprocity.

Findings

Rousseau's proof of quadratic reciprocity is straightforward.

Quadratic reciprocity is shown to be equivalent to Hilbert's product formula.

The places of Q are explicitly determined in this context.

Abstract

Rousseau's simple proof of the quadratic reciprocity law, followed by the proof of its equivalence with Hilbert's product formula. The Hilbert symbol is explained in terms of the reciprocity isomorphism, and the places of Q are determined.