Atıf İçin Kopyala
Badziahin D., Schleischitz J.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.374, sa.3, ss.1847-1861, 2021 (SCI-Expanded)
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Yayın Türü:
Makale / Tam Makale
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Cilt numarası:
374
Sayı:
3
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Basım Tarihi:
2021
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Doi Numarası:
10.1090/tran/8245
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Dergi Adı:
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
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Derginin Tarandığı İndeksler:
Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
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Sayfa Sayıları:
ss.1847-1861
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Anahtar Kelimeler:
Wirsing's problem, exponents of Diophantine approximation, CUBIC ALGEBRAIC-INTEGERS, DIOPHANTINE APPROXIMATION, REAL NUMBERS, PARAMETRIC GEOMETRY, EXPONENTS
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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.