Notes on asymptotic eigenvalues distribution on complex circles

TL;DR

This paper investigates the asymptotic distribution of eigenvalues on complex circles by connecting concepts from algebraic geometry and linear algebra, focusing on Frobenius roots and spectral distributions.

Contribution

It establishes a theoretical link between eigenvalue distributions in linear algebra and Frobenius root distributions in algebraic geometry, bridging two mathematical areas.

Findings

Links spectral distributions with Frobenius root distributions

Provides measure-theoretic framework for eigenvalue analysis

Bridges finite field curves and matrix spectral theory

Abstract

With tools of measure theory and symbols of matrix sequences, we explore the results regarding curves on finite fields and Weil Systems. This document wants to draw a bridge between the two areas and link the concepts of distribution of Frobenius roots in the context of Zeta functions on curves, with the spectral distributions already studied in linear algebra.