Multiplicative parametric geometry of numbers and transference theorems for lattice exponents

2018/12/06 by Oleg N. German, German, Oleg N.
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1812.02774

openalex publication_date 2018/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we adapt parametric geometry of numbers developed by Wolfgang Schmidt and Leonard Summerer to a multiplicative setting, and derive a chain of inequalities for the corresponding exponents which splits the transference inequality for Diophantine exponents of lattices in the same way Khintchine's transference inequalities for simultaneous approximation can be split.

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