Harbingers of Artin's Reciprocity Law. III. Gauss's Lemma and Artin's Transfer

TL;DR

This paper explores the connections between Artin's reciprocity law and quadratic reciprocity, focusing on Gauss's Lemma, and provides insights into classical ideal theoretic approaches.

Contribution

It offers a detailed analysis linking Artin's reciprocity law with proofs of quadratic reciprocity via Gauss's Lemma, enriching the theoretical understanding.

Findings

Clarifies the relationship between Artin's law and quadratic reciprocity

Highlights the role of Gauss's Lemma in classical proofs

Provides a unified perspective on ideal theoretic approaches

Abstract

We briefly review Artin's reciprocity law in the classical ideal theoretic language, and then study connections between Artin's reciprocity law and the proofs of the quadratic reciprocity law using Gauss's Lemma.