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Very recently, the generating function $A (z)$ of the Stern sequence ${(a_{n})}_{n \geq 0}$ , defined by $a_{0} : = 0, a_{1} : = 1,$ and $a_{2 n} : = a_{n}, a_{2 n + 1} : = a_{n} + a_{n + 1}$ for any integer $n > 0$ , has been considered from the arithmetical point of view. Coons [8] proved the transcendence of $A (α)$ for every algebraic $α$ with $0 < | α | < 1$ , and this result was generalized in [6] to the effect that, for the same $α$ ’s, all numbers $A (α), A^{'} (α), A^{''} (α), ...$ are algebraically independent. At about the same time, Bacher [4] studied the twisted version $(b_{n})$ of Stern’s sequence, defined by $b_{0} : = 0, b_{1} : = 1,$ and $b_{2 n} : = - b_{n}, b_{2 n + 1} : = - (b_{n} + b_{n + 1})$ for any $n > 0$ .The aim of our paper is to show...

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Actions of sets of integers on irrationals

Addendum to "Continued fractions of some algebraic numbers".

Addendum to “On the $p^{λ}$ problem”

Addendum to the article: Polylogarithms in the field of omega (a root of a given cubic): Functional equations and ladders.

Addendum to the paper:"On two theorems of Gelfond and some of their applications" (Acta Arith. 13 (1967), pp. 177-236)

Algebraic continued fractions in $_{q} ((T^{- 1}))$ and recurrent sequences in $_{q}$

Algebraic independence by Mahler’s method and $S$ -unit equations

Algebraic independence measures of the values of Mahler functions.

Algebraic independence of elementary functions and its application to Masser's vanishing theorem.

Algebraic independence of elements from ℂₚ over ℚₚ, II

Algebraic independence of Fredholm series

Algebraic independence of real numbers with low density of nonzero digits

Algebraic Independence of Reciprocal Sums of Binary Recurrences.

Algebraic independence of the generating functions of Stern’s sequence and of its twist

Algebraic independence of the numbers $\prod_{K = 0}^{\infty} (1 - p^{- 2^{K}})$ with $p$ prime

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

Algebraic independence of the values of certain functions at a transcendental number

Algebraic Independence of the Values of Certain Series by Mahler's Method.

Algebraic Independence of the Values of Elliptic Function at Algebraic Points.

Algebraic independence of the values of generalized Mahler functions

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