On irrationality measure functions for several real numbers

TL;DR

This paper investigates the mutual behavior of irrationality measure functions for multiple real numbers, providing new insights into their combined approximation properties.

Contribution

It introduces a novel result describing the joint behavior of irrationality measure functions for several real numbers.

Findings

New theoretical bounds on the mutual behavior of irrationality measures

Enhanced understanding of simultaneous Diophantine approximation

Potential applications to number theory problems

Abstract

We prove a new result about the mutual behavior of irrationality measure functions $\psi_{\alpha_j}(t)$ for $n$ different real numbers $\alpha_j, j = 1, \dots, n$.