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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 374 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1090/tran/8245
  • Title of Journal : TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.1847-1861

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.