A certain power series associatedwith a Beatty sequence

• Autorzy: Takao Komatsu
• Języki publikacji: EN

Kategorie tematyczne

• 11B83: Special sequences and polynomials

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996
• Tom: 76
• Numer: 2
• Strony: 109-129

Daty

wydano

1996

otrzymano

1994-10-06

poprawiono

1995-08-09

Twórcy

autor

Takao Komatsu

• School of Mathematics, Physics, Computing and Electronics, Macquarie University, Sydney, New South Wales 2109, Australia

Bibliografia

• [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.
• [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] 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.
• [4] T. Komatsu, On the characteristic word of the inhomogeneous Beatty sequence, Bull. Austral. Math. Soc. 51 (1995), 337-351.
• [5] T. Komatsu, The fractional part of nθ+ϕ and Beatty sequences, J. Théorie des Nombres de Bordeaux 7 (1995), 387-406.
• [6] T. Komatsu, A certain power series and the inhomogeneous continued fraction expansions, J. Number Theory, to appear.
• [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.
• [8] K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366.
• [9] K. Nishioka, I. Shiokawa and J. Tamura, Arithmetical properties of a certain power series, J. Number Theory 42 (1992), 61-87.
• [10] B. A. Venkov, Elementary Number Theory, Wolters-Noordhoff, Groningen, 1970.