A General Reciprocity Law on arbitrary Vector Spaces

TL;DR

This paper introduces a broad theoretical framework for reciprocity laws applicable to arbitrary vector spaces, aiming to unify and extend existing reciprocity principles across different mathematical contexts.

Contribution

It presents a new general theory of reciprocity laws that applies to all vector spaces, expanding the scope of classical reciprocity concepts.

Findings

Developed a unified reciprocity framework for vector spaces

Extended classical reciprocity laws to a general setting

Provided foundational results for future research in the area

Abstract

The paper contained a preliminary version of a general theory of reciprocity laws on vector spaces.