AN IMPROVED BOUND IN WIRSING'S PROBLEM
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.374, sa.3, ss.1847-1861, 2021 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 374 Sayı: 3
- Basım Tarihi: 2021
- Doi Numarası: 10.1090/tran/8245
- Dergi Adı: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
- Sayfa Sayıları: ss.1847-1861
- Anahtar Kelimeler: Wirsing's problem, exponents of Diophantine approximation, CUBIC ALGEBRAIC-INTEGERS, DIOPHANTINE APPROXIMATION, REAL NUMBERS, PARAMETRIC GEOMETRY, EXPONENTS
- Orta Doğu Teknik Üniversitesi Adresli: Evet
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.