AN IMPROVED BOUND IN WIRSING'S PROBLEM


Badziahin D., Schleischitz J.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.374, sa.3, ss.1847-1861, 2021 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 374 Konu: 3
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1090/tran/8245
  • Dergi Adı: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.1847-1861

Özet

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.