Algebraic independence of the values at algebraic points of a class of functions considered by Mahler

The example of the boundary of a square shows that the exponent r = 2 is, in general, best possible. We conclude this note by sketching an alternate proof of 2) implies 1)

Stankiewicz, On a class of p-valent analytic functions with fixed argument of coefficients defined by fractional calculus, Folia Scient. Waniurski, Some classes of univalent

Besides standard facts in analytic and algebraic geometry, the main points in the proof of Theorem 1 are Proposition 2.1 and the above-an- nounced result from [C], which may

thence is derived a general result (Theorem 3.2) to the effect that when- ever the d-function is bounded, common extensions of consistent charges always exist, irrespective of the

This work was supported in part by the Japanese Ministry of Education, Science and Culture under Grant-in-Aid for General Scientific

The author wishes to thank the referee for helpful comments and suggestions, and especially for pointing out several mistakes and a direct proof of the

In view of the existence of correlations between the approximation of zero by values of integral polynomials and approximation of real numbers by algebraic numbers, we are interested

In analogy to Lemma 2.1 the integral on the left-hand side exists since the boundary lies in a finite union of hyperplanes... Heights and