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

Christoph Baxa

Acta Arithmetica (1997)

  • Volume: 81, Issue: 4, page 357-363
  • ISSN: 0065-1036

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Christoph Baxa. "On the distribution of the sequence (nα) with transcendental α." Acta Arithmetica 81.4 (1997): 357-363. <http://eudml.org/doc/207070>.

@article{ChristophBaxa1997,
author = {Christoph Baxa},
journal = {Acta Arithmetica},
keywords = {transcendence; distribution of sequences; irrational of bounded density; star-discrepancy},
language = {eng},
number = {4},
pages = {357-363},
title = {On the distribution of the sequence (nα) with transcendental α},
url = {http://eudml.org/doc/207070},
volume = {81},
year = {1997},
}

TY - JOUR
AU - Christoph Baxa
TI - On the distribution of the sequence (nα) with transcendental α
JO - Acta Arithmetica
PY - 1997
VL - 81
IS - 4
SP - 357
EP - 363
LA - eng
KW - transcendence; distribution of sequences; irrational of bounded density; star-discrepancy
UR - http://eudml.org/doc/207070
ER -

References

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  1. [1] A. Baker, Continued fractions of transcendental numbers, Mathematika 9 (1962), 1-8. Zbl0105.03903
  2. [2] A. Baker, On Mahler's classification of transcendental numbers, Acta Math. 111 (1964), 97-120. Zbl0147.03403
  3. [3] C. Baxa, On the discrepancy of the sequence (nα), J. Number Theory 55 (1995), 94-107. Zbl0835.11028
  4. [4] H. Behnke, Zur Theorie der diophantischen Approximationen I, Abh. Math. Sem. Univ. Hamburg 3 (1924), 261-318. Zbl50.0124.03
  5. [5] P. Bohl, Über ein in der Theorie der säkularen Störungen vorkommendes Problem, J. Reine Angew. Math. 135 (1909), 189-283. Zbl40.1005.03
  6. [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. [7] E. Maillet, Introduction à la théorie des nombres transcendants et des propriétés arithmétiques des fonctions, Gauthier-Villars, Paris, 1906. Zbl37.0237.02
  8. [8] O. Perron, Die Lehre von den Kettenbrüchen, Band 1, Teubner, Stuttgart, 1977. Zbl43.0283.04
  9. [9] W. M. Schmidt, On simultaneous approximations of two algebraic numbers by rationals, Acta Math. 119 (1967), 27-50. Zbl0173.04801
  10. [10] W. M. Schmidt, Simultaneous approximation to algebraic numbers by rationals, ibid. 125 (1970), 189-201. Zbl0205.06702
  11. [11] W. M. Schmidt, Irregularities of distribution VII, Acta Arith. 21 (1972), 45-50. Zbl0244.10035
  12. [12] W. M. Schmidt, Diophantine Approximation, Lecture Notes in Math. 785, Springer, Berlin, 1980. Zbl0421.10019
  13. [13] J. Schoißengeier, On the discrepancy of (nα) II, J. Number Theory 24 (1986), 54-64. Zbl0588.10058
  14. [14] J. Schoißengeier, The discrepancy of ( n α ) n ≥ 1 , Math. Ann. 296 (1993), 529-545. Zbl0786.11043
  15. [15] W. Sierpiński, Sur la valeur asymptotique d'une certaine somme, Bull. Internat. Acad. Polon. Sci. Lettres Sér. A Sci. Math. 1910, 9-11. Zbl41.0282.01
  16. [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. [17] H. Weyl, Über die Gibbs'sche Erscheinung und verwandte Konvergenzphänomene, Rend. Circ. Mat. Palermo 30 (1910), 377-407. Zbl41.0528.02
  18. [18] H. Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352. Zbl46.0278.06

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