## Rational approximations to $$\pi$$ and some other numbers.(English)Zbl 0776.11033

The author proves the irrationality measure 4.6016 for $$n/\sqrt 3$$ and 8.0161 for $$\pi$$ and $$\pi/\log 2$$. The proof is based on the expression of the integral $\int_ \Gamma ((z-a_ 1)^ 2(z-a_ 2)^ 2(z-a_ 3)^ 2/z^ 3)^ n dz/z$ as a sum of simple integrals for suitable numbers $$a_ 1$$, $$a_ 2$$ and $$a_ 3$$. Similarly the author obtains the linear independence measure for 1, $$n\sqrt 3$$, $$\log(3,4)$$, and some other results. Let us note, that the above measures contain roots of cubic equations with integral coefficients.
Reviewer: J.Hančl (Ostrava)

### MSC:

 11J82 Measures of irrationality and of transcendence 11J72 Irrationality; linear independence over a field

### Keywords:

irrationality measure; linear independence measure
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