On simultaneous approximation of the values of certain Mahler functions

Abstract

In this paper, we estimate the simultaneous approximation exponents of the values of certain Mahler functions. For this we construct Hermite-Padé approximations of the functions under consideration, then apply the functional equations to get an infinite sequence of approximations and use the numerical approximations obtained from this sequence.

On linear independence measures of the values of Mahler functions

“…This work is a continuation to [14], where we studied simultaneous approximations of similar numbers γ 1 and γ 2 . We also note that, after Bugeaud's remarkable work [4] on Thue-Morse numbers, there has appeared several works on the irrationality exponents of the values of degree one Mahler functions, see [2,5,9,11,13,15] and the references in [5].…”

“…Note also that, in [7], an upper bound 5 is obtained for the irrationality exponent of S(1/b). This work is a continuation of [14], in which we the studied simultaneous approximations of similar numbers. These results and Khintchine's transference theorem can be used to obtain linear independence measures for the numbers in theorems 1.3, 1.4 and 1.6, but the results are weaker than those obtained in this paper.…”