Extremal numbers and multi-parametric geometry of numbers
Damien Roy
TL;DR
This paper investigates the approximation of points like (1, ξ, ξ^2) for extremal real numbers using multi-parametric geometry of numbers, advancing understanding of Diophantine approximation in this context.
Contribution
It introduces a new framework for weighted simultaneous approximation to algebraic points using multi-parametric geometry of numbers, focusing on extremal real numbers.
Findings
Characterization of approximation properties for extremal numbers
Development of a multi-parametric geometric approach
New bounds on approximation quality
Abstract
We study weighted simultaneous rational approximation to points of the form , for a class of extremal real numbers , within the framework of multi-parametric geometry of numbers.
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Taxonomy
TopicsAdvanced Banach Space Theory · Mathematical Dynamics and Fractals · Holomorphic and Operator Theory