On inhomogeneous diophantine approximation with some quasi-periodic expressions, II
Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 2, pp. 331-344

We consider the values concerning

ℳ(θ,φ)=lim inf |q|→∞ |q|||q θ -φ||
where the continued fraction expansion of θ has a quasi-periodic form. In particular, we treat the cases so that each quasi-periodic form includes no constant. Furthermore, we give some general conditions satisfying ℳ(θ,φ)=0.

On s’intéresse aux valeurs de

ℳ(θ,φ)=lim inf |q|→∞ |q|||q θ -φ||
lorsque θ est un réel ayant un développement en fraction continue quasi-périodique.

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     author = {Takao Komatsu},
     title = {On inhomogeneous diophantine approximation with some quasi-periodic expressions, {II}},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {331--344},
     year = {1999},
     publisher = {Universit\'e Bordeaux I},
     volume = {11},
     number = {2},
     zbl = {1058.11049},
     mrnumber = {1745883},
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Takao Komatsu. On inhomogeneous diophantine approximation with some quasi-periodic expressions, II. Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 2, pp. 331-344. https://jtnb.centre-mersenne.org/item/JTNB_1999__11_2_331_0/

[1] J.W.S. Cassels, Über limx→+∞x|ϑx + α - y|. Math. Ann. 127 (1954), 288-304. | Zbl

[2] T W. Cusick, A. M. Rockett and P. Szüsz, On inhomogeneous Diophantine approximation. J. Number Theory 48 (1994), 259-283. | Zbl | MR

[3] C.S. Davis On some simple continued fractions connected with e. J. London Math. Soc. 20 (1945), 194-198. | Zbl | MR

[4] R. Descombes Sur la répartition des sommets d'une ligne polygonale régulière non fermée. Ann. Sci. École Norm Sup. 73 (1956), 283-355. | Zbl | MR | Numdam

[5] T. Komatsu On Inhomogeneous continued fraction expansion and inhomogeneous Diophantine approximation. J. Number Theory 62 (1997), 192-212. | Zbl | MR

[6] T. Komatsu On inhomogeneous Diophantine approximation and the Nishioka-Shiokawa-Tamura algorithm. Acta Arith. 86 (1998), 305-324. | Zbl | MR

[7] T. Komatsu On inhomogeneous Diophantine approximation with some quasi-periodic expressions. Acta Math. Hung. 85 (1999), 303-322. | Zbl | MR

[8] K.R. Matthews and R.F.C. Walters Some properties of the continued fraction expansion of (m/n)e1/q. Proc. Cambridge Philos. Soc. 67 (1970), 67-74. | Zbl | MR

[9] K. Nishioka, I. Shiokawa and J. Tamura Arithmetical properties of a certain power series. J. Number Theory 42 (1992), 61-87. | Zbl | MR

[10] O. Perron Die Lehre von den Kettenbrüchen. Chelsea reprint of 1929 edition. | Zbl

[11] V.T. Sós On the theory of Diophantine approximations, II. Acta Math. Acad. Sci. Hung. 9 (1958), 229-241. | Zbl | MR