A certain power series associatedwith a Beatty sequence

Takao Komatsu

Acta Arithmetica (1996)

  • Volume: 76, Issue: 2, page 109-129
  • ISSN: 0065-1036

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Takao Komatsu. "A certain power series associatedwith a Beatty sequence." Acta Arithmetica 76.2 (1996): 109-129. <http://eudml.org/doc/206889>.

@article{TakaoKomatsu1996,
author = {Takao Komatsu},
journal = {Acta Arithmetica},
keywords = {power series; Beatty sequence},
language = {eng},
number = {2},
pages = {109-129},
title = {A certain power series associatedwith a Beatty sequence},
url = {http://eudml.org/doc/206889},
volume = {76},
year = {1996},
}

TY - JOUR
AU - Takao Komatsu
TI - A certain power series associatedwith a Beatty sequence
JO - Acta Arithmetica
PY - 1996
VL - 76
IS - 2
SP - 109
EP - 129
LA - eng
KW - power series; Beatty sequence
UR - http://eudml.org/doc/206889
ER -

References

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  1. [1] P. Bundschuh, Über eine Klasse reeller Transzendenter Zahlen mit explicit angebbarer g-adischer und Kettenbruch-Entwicklung, J. Reine Angew. Math. 318 (1980), 110-119. Zbl0425.10038
  2. [2] A. S. Fraenkel, M. Mushkin and U. Tassa, Determination of [nθ] by its sequence of differences, Canad. Math. Bull. 21 (1978), 441-446. 
  3. [3] S. Ito and S. Yasutomi, On continued fractions, substitutions and characteristic sequences [nx+y]-[(n-1)x+y], Japan. J. Math. 16 (1990), 287-306. Zbl0721.11009
  4. [4] T. Komatsu, On the characteristic word of the inhomogeneous Beatty sequence, Bull. Austral. Math. Soc. 51 (1995), 337-351. Zbl0829.11012
  5. [5] T. Komatsu, The fractional part of nθ+ϕ and Beatty sequences, J. Théorie des Nombres de Bordeaux 7 (1995), 387-406. Zbl0849.11027
  6. [6] T. Komatsu, A certain power series and the inhomogeneous continued fraction expansions, J. Number Theory, to appear. Zbl0872.11033
  7. [7] J. H. Loxton and A. J. van der Poorten, Arithmetic properties of certain functions in several variables, III, Bull. Austral. Math. Soc. 16 (1977), 15-47. Zbl0339.10028
  8. [8] K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366. Zbl55.0115.01
  9. [9] K. Nishioka, I. Shiokawa and J. Tamura, Arithmetical properties of a certain power series, J. Number Theory 42 (1992), 61-87. Zbl0770.11039
  10. [10] B. A. Venkov, Elementary Number Theory, Wolters-Noordhoff, Groningen, 1970. 

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