On the weak uniform Diophantine exponent of a real number

TL;DR

This paper introduces the concept of a weak uniform Diophantine exponent for real numbers and provides a complete characterization of its possible values.

Contribution

It defines a new Diophantine exponent and fully describes its spectrum of values, advancing understanding in Diophantine approximation theory.

Findings

Complete description of the spectrum of the weak uniform Diophantine exponent.

Introduction of a new Diophantine exponent concept.

Theoretical framework for analyzing Diophantine exponents.

Abstract

In this paper we introduce the notion of a weak uniform Diophantine exponent of a real number and obtain the complete description of the spectrum of its values.