ON WIRSING’S PROBLEM IN SMALL EXACT DEGREE

SCHLEISCHITZ J.

Moscow Mathematical Journal, cilt.24, sa.3, ss.461-489, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 3
  • Basım Tarihi: 2024
  • Doi Numarası: 10.17323/1609-4514-2024-24-3-461-489
  • Dergi Adı: Moscow Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.461-489
  • Anahtar Kelimeler: Exponents of Diophantine approximation, Irreducibility of integer polynomials, Wirsing’s problem
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We investigate a variant of Wirsing’s problem on approximation to a real number by real algebraic numbers of degree exactly n. This has been studied by Bugeaud and Teulie. We improve their bounds for degrees up to n = 7. Moreover, we obtain results regarding small values of polynomials and approximation to a real number by algebraic integers and units in small prescribed degree. The main ingredient are irreducibility criteria for integral linear combinations of coprime integer polynomials. Moreover, for cubic polynomials, these criteria improve results of Győry on a problem of Szegedy.