On a Conjecture of Schmidt for the Parametric Geometry of Numbers

2015/12/09 by Aminata Dite Tanti Keita, Keita, Aminata Dite Tanti
Mathematics · #11J04 #11J82 #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1512.02939

openalex publication_date 2015/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Continued fractions and parametric geometry of numbers
• Multiplicative parametric geometry of numbers and transference theorems for lattice exponents
• Parametric geometry of numbers over a number field and extension of scalars
• A Minkowski-type theorem on distances to cusps: the class number one case
• Schmidt's conjecture and Badziahin-Pollington-Velani's theorem