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On inhomogeneous diophantine approximation and the Nishioka-Shiokawa-Tamura algorithm. (English) Zbl 0930.11049
Given a real $$\varphi$$ and an irrational $$\vartheta$$ such that $$q\vartheta-\varphi$$ is not integral for any integer $$q$$, let $${\mathcal M}(\vartheta,\varphi)=\lim\inf_{|q|\to\infty}(q\|q\vartheta-\varphi\|)$$ be the inhomogeneous approximation constant for the pair $$\vartheta,\varphi$$. The author uses an algorithm by K. Nishioka, I. Shiokawa and J. Tamura [J. Number Theory 42, 61-87 (1992; Zbl 0770.11039)] which represents $$\varphi$$ in terms of the continued fraction expansion of $$\vartheta$$ to evaluate $${\mathcal M}(\vartheta,\varphi)$$ for certain classes of pairs such as $$\vartheta=(\sqrt{ab(ab+4)}-ab)/(2a)$$ and $$\varphi=1/a$$ or $$\varphi=1/\sqrt{ab(ab+4)}$$. (For earlier work by the author on the same subject see [J. Number Theory 62, 192-212 (1997; Zbl 0878.11029)]).

##### MSC:
 11J20 Inhomogeneous linear forms 11J70 Continued fractions and generalizations
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