ArticleOriginal scientific text

Title

On the distribution of the sequence (nα) with transcendental α

Authors 1

Affiliations

  1. Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria

Bibliography

  1. A. Baker, Continued fractions of transcendental numbers, Mathematika 9 (1962), 1-8.
  2. A. Baker, On Mahler's classification of transcendental numbers, Acta Math. 111 (1964), 97-120.
  3. C. Baxa, On the discrepancy of the sequence (nα), J. Number Theory 55 (1995), 94-107.
  4. H. Behnke, Zur Theorie der diophantischen Approximationen I, Abh. Math. Sem. Univ. Hamburg 3 (1924), 261-318.
  5. P. Bohl, Über ein in der Theorie der säkularen Störungen vorkommendes Problem, J. Reine Angew. Math. 135 (1909), 189-283.
  6. Y. Dupain and V. T. Sós, On the discrepancy of (nα) sequences, in: Topics in Classical Number Theory, Vol. 1, Colloq. Math. Soc. János Bolyai 34, G. Halász (ed.), North-Holland, Amsterdam, 1984, 355-387.
  7. E. Maillet, Introduction à la théorie des nombres transcendants et des propriétés arithmétiques des fonctions, Gauthier-Villars, Paris, 1906.
  8. O. Perron, Die Lehre von den Kettenbrüchen, Band 1, Teubner, Stuttgart, 1977.
  9. W. M. Schmidt, On simultaneous approximations of two algebraic numbers by rationals, Acta Math. 119 (1967), 27-50.
  10. W. M. Schmidt, Simultaneous approximation to algebraic numbers by rationals, ibid. 125 (1970), 189-201.
  11. W. M. Schmidt, Irregularities of distribution VII, Acta Arith. 21 (1972), 45-50.
  12. W. M. Schmidt, Diophantine Approximation, Lecture Notes in Math. 785, Springer, Berlin, 1980.
  13. J. Schoißengeier, On the discrepancy of (nα) II, J. Number Theory 24 (1986), 54-64.
  14. J. Schoißengeier, The discrepancy of (nα)n1, Math. Ann. 296 (1993), 529-545.
  15. W. Sierpiński, Sur la valeur asymptotique d'une certaine somme, Bull. Internat. Acad. Polon. Sci. Lettres Sér. A Sci. Math. 1910, 9-11.
  16. W. Sierpiński, On the asymptotic value of a certain sum, Rozprawy Akademii Umiej/etno/sci w Krakowie, Wydzia/l mat. przyrod. 50 (1910), 1-10 (in Polish).
  17. H. Weyl, Über die Gibbs'sche Erscheinung und verwandte Konvergenzphänomene, Rend. Circ. Mat. Palermo 30 (1910), 377-407.
  18. H. Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352.
Pages:
357-363
Main language of publication
English
Received
1996-10-08
Accepted
1997-04-03
Published
1997
Exact and natural sciences