On a Conjecture of Schmidt for the Parametric Geometry of Numbers
Aminata Dite Tanti Keita
TL;DR
This paper leverages the parametric geometry of numbers to prove a strong version of Schmidt's conjecture related to the successive minima of a lattice, advancing understanding in this area.
Contribution
It introduces a proof of a strong form of Schmidt's conjecture using the parametric geometry of numbers, a recent theoretical framework.
Findings
Proves a strong version of Schmidt's conjecture.
Establishes new bounds for successive minima.
Enhances the theoretical understanding of lattice geometry.
Abstract
With the help of the recently introduced parametric geometry of numbers by W. M. Schmidt and L. Summerer, we prove a strong version of a conjecture of Schmidt concerning the successive minima of a lattice.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Mathematics and Applications · Analytic Number Theory Research