Derived Langlands VIII: Local GLn

TL;DR

This paper introduces a 2-variable L-function for representations of local GLn groups, advancing the Derived Langlands series despite incomplete proofs due to health issues.

Contribution

It presents a novel construction of a 2-variable L-function for local GLn representations, expanding the theoretical framework of the Derived Langlands program.

Findings

Proposed a new 2-variable L-function construction

Extended the Derived Langlands series to local fields

Provided preliminary ideas and suggestive proofs

Abstract

In this, the eighth article in my Derived Langlands series, I describe the construction of a 2-variable L-function for two representations of general linear groups of a $p$-adic local field. Due to extenuating health circumstances, many of the proofs and ideas herein are suggestive rather than the finished definitive versions.