Non-Abelian L Function for Number Fields

TL;DR

This paper introduces non-abelian L-functions for number fields using geo-arithmetical methods and Langlands' theory, expanding the understanding of zeta functions beyond abelian cases.

Contribution

It presents a novel framework for non-abelian L-functions for number fields based on geo-arithmetical cohomology and Langlands' Eisenstein series.

Findings

Defined non-abelian zeta functions for number fields

Established connections with geo-arithmetical cohomology

Laid groundwork for further research in non-abelian number theory

Abstract

This is an integrated part of our Geo-Arithmetic Program. In this paper we introduce and hence study non-abelian zeta functions and more generally non-abelian $L$-functions for number fields, based on geo-arithmetical cohomology, geo-arithmetical truncation and Langlands' theory of Eisenstein series.