## Approximation to certain transcendental decimal fractions by algebraic numbers.(English)Zbl 0718.11030

For a positive integer $$g\geq 2$$ consider the number $$M(g)=0.(1)_ g(2)_ g...(n)_ g...$$ where for $$n\in {\mathbb{N}}$$ $$(n)_ g$$ means digit representation of n to base g and $$0.(1)_ g(2)_ g...$$ means digit representation of the real M(g) to base g. It is known that M(g) is transcendental. The author gives estimates for Mahler’s function $$w_ d$$ and for Koksma’s function $$w^*_ d$$ of this number and he determines the exact value of the irrationality measure $$\mu (M(g)):=w_ 1(M(g))+1=w^*_ 1(M(g))+1$$ of M(g), namely $$\mu M(g))=g$$ for any $$g\geq 2$$. Until now it was only known that $$\mu (M(g))\leq 2g^ 2/(g-1)$$.

### MSC:

 11J82 Measures of irrationality and of transcendence 11J17 Approximation by numbers from a fixed field 11A63 Radix representation; digital problems
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### References:

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