Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On $U_{m}$-numbers
HTML articles powered by AMS MathViewer

by K. Alniaçik
Proc. Amer. Math. Soc. 85 (1982), 499-505
DOI: https://doi.org/10.1090/S0002-9939-1982-0660590-X

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
  • 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
  • Alan Baker, Transcendental number theory, Cambridge University Press, London-New York, 1975. MR 0422171, DOI 10.1017/CBO9780511565977
  • 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
  • R. Güting, Approximation of algebraic number by algebraic numbers, Michigan Math. J. 8 (1951), 149-159.
  • 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 389777
  • 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 845, DOI 10.1007/BF01696176
  • W. J. LeVeque, On Mahler’s $U$-numbers, J. London Math. Soc. 28 (1953), 220–229. MR 54658, DOI 10.1112/jlms/s1-28.2.220
  • —, Topics in number theory. Vol. II, Addison-Wesley, Reading, Mass., 1956. K. Mahler, Zur Approximation der Exponential Funktion und des logarithmus. I, J. Reine Angew. Math. 166 (1932), 118-136.
  • Eduard Wirsing, Approximation mit algebraischen Zahlen beschränkten Grades, J. Reine Angew. Math. 206 (1961), 67–77 (German). MR 142510, DOI 10.1515/crll.1961.206.67
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10F20, 10F35
  • Retrieve articles in all journals with MSC: 10F20, 10F35
Bibliographic Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 499-505
  • MSC: Primary 10F20; Secondary 10F35
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0660590-X
  • MathSciNet review: 660590