AN IMPROVED BOUND IN WIRSING'S PROBLEM

Badziahin D., Schleischitz J.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.374, no.3, pp.1847-1861, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 374 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1090/tran/8245
  • Journal Name: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.1847-1861
  • Keywords: Wirsing's problem, exponents of Diophantine approximation, CUBIC ALGEBRAIC-INTEGERS, DIOPHANTINE APPROXIMATION, REAL NUMBERS, PARAMETRIC GEOMETRY, EXPONENTS
  • Middle East Technical University Affiliated: Yes

Abstract

We improve the lower bound for the classical exponent of approximation w(n)* connected to Wirsing's famous problem on approximation to real numbers by algebraic numbers of degree at most n. Our bound exceeds n/root 3 approximate to 0.5773n and thus provides a considerable qualitative improvement to previous bounds of order n/2 + O(1). We further establish new relations between several classical exponents of approximation.