Scholz's reciprocity law in number fields

TL;DR

This paper proves a reciprocity law in number fields with odd class number, generalizing Scholz's reciprocity law from the rational numbers to a broader class of number fields.

Contribution

It introduces a new reciprocity law applicable to number fields with odd class number, extending Scholz's classical result.

Findings

Established a reciprocity law in number fields with odd class number

Generalized Scholz's reciprocity law from rationals to number fields

Provides a theoretical foundation for further algebraic number theory research

Abstract

In this article we prove a reciprocity law in number fields with odd class number that specializes to Scholz's reciprocity law over the rationals.