Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On $ U\sb{m}$-numbers


Author: K. Alniaçik
Journal: Proc. Amer. Math. Soc. 85 (1982), 499-505
MSC: Primary 10F20; Secondary 10F35
MathSciNet review: 660590
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we shall give some examples of $ {U_m}$-numbers by using the continued fraction expansions of algebraic numbers of degree $ m > 1$.


References [Enhancements On Off] (What's this?)

  • [1] K. Alniaçik, On 𝑝-adic 𝑈_{𝑚}-numbers, İstanbul Üniv. Fen Fak. Mat. Derg. 50 (1991), 1–7 (1993) (English, with English and Turkish summaries). MR 1270564 (95d:11084)
  • [2] Alan Baker, Transcendental number theory, Cambridge University Press, London-New York, 1975. MR 0422171 (54 #10163)
  • [3] J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 45, Cambridge University Press, New York, 1957. MR 0087708 (19,396h)
  • [4] R. Güting, Approximation of algebraic number by algebraic numbers, Michigan Math. J. 8 (1951), 149-159.
  • [5] Orhan Ş. İçen, Anhang zu den Arbeiten “Über die Funktionswerte der 𝑝-adisch elliptischen Funktionen. I, II” (İstanbul Üniv. Fen Fak. Mecm. Ser. A 36 (1971), 53–87 (1974); ibid. 35 (1970), 139–166 (1972)), İstanbul Üniv. Fen Fak. Mecm. Ser. A 38 (1973), 25–35 (1975) (German, with Turkish summary). MR 0389777 (52 #10608)
  • [6] J. F. Koksma, Über die Mahlersche Klasseneinteilung der transzendenten Zahlen und die Approximation komplexer Zahlen durch algebraische Zahlen, Monatsh. Math. Phys. 48 (1939), 176–189 (German). MR 0000845 (1,137a)
  • [7] W. J. LeVeque, On Mahler’s 𝑈-numbers, J. London Math. Soc. 28 (1953), 220–229. MR 0054658 (14,956e)
  • [8] -, Topics in number theory. Vol. II, Addison-Wesley, Reading, Mass., 1956.
  • [9] K. Mahler, Zur Approximation der Exponential Funktion und des logarithmus. I, J. Reine Angew. Math. 166 (1932), 118-136.
  • [10] Eduard Wirsing, Approximation mit algebraischen Zahlen beschränkten Grades, J. Reine Angew. Math. 206 (1960), 67–77 (German). MR 0142510 (26 #79)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10F20, 10F35

Retrieve articles in all journals with MSC: 10F20, 10F35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660590-X
PII: S 0002-9939(1982)0660590-X
Article copyright: © Copyright 1982 American Mathematical Society