Computing L-functions of $ λ$-adic representations of global function fields
Abstract
The L-function $ L(ρ_λ, s) $ of an almost everywhere unramified $ λ$-adic representation $ ρ_λ$ of a global function field $ \mathbb{F}_q(C) $ is known to be a rational function in $ q^{-s} $ satisfying a functional equation up to some complex sign $ ε(ρ_λ) $. This paper presents a systematic framework to compute the coefficients of $ L(ρ_λ, s) $ and its sign $ ε(ρ_λ) $ with some explicit examples.
Fields of Study & Subjects
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Analytic Number Theory Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 25 January 2026
- Document type
- Preprint