Nerves and set-theoretical independence
B. Węglorz (1964)
Colloquium Mathematicae
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B. Węglorz (1964)
Colloquium Mathematicae
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Peter Bundschuh, Keijo Väänänen (2005)
Acta Arithmetica
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Jaroslav Hančl, Robert Tijdeman (2005)
Acta Arithmetica
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D. Ramachandran (1975)
Colloquium Mathematicae
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K. Golema-Hartman (1976)
Colloquium Mathematicae
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Jaroslav Hančl (1996)
Mathematica Slovaca
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A. J. van der POORTEN (1982-1983)
Seminaire de Théorie des Nombres de Bordeaux
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Kazimierz Głazek (1979)
Colloquium Mathematicae
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Alina Firicel (2013)
Acta Arithmetica
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We give a general upper bound for the irrationality exponent of algebraic Laurent series with coefficients in a finite field. Our proof is based on a method introduced in a different framework by Adamczewski and Cassaigne. It makes use of automata theory and, in our context, of a classical theorem due to Christol. We then introduce a new approach which allows us to strongly improve this general bound in many cases. As an illustration, we give a few examples of algebraic Laurent series...
Peter Bundschuh, Keijo Väänänen (2014)
Acta Arithmetica
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This article continues two papers which recently appeared in this same journal. First, Dilcher and Stolarsky [140 (2009)] introduced two new power series, F(z) and G(z), related to the so-called Stern polynomials and having coefficients 0 and 1 only. Shortly later, Adamczewski [142 (2010)] proved, inter alia, that G(α),G(α⁴) are algebraically independent for any algebraic α with 0 < |α| < 1. Our first key result is that F and G have large blocks of consecutive zero coefficients....
Mamoru Takeuchi (2005)
Acta Arithmetica
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Iekata SHIOKAWA (1980-1981)
Seminaire de Théorie des Nombres de Bordeaux
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Kumiko Nishioka (1991)
Journal für die reine und angewandte Mathematik
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Daniel Duverney, Kumiko Nishioka (2003)
Acta Arithmetica
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Alfred POORTEN van der (1975-1976)
Seminaire de Théorie des Nombres de Bordeaux
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Iekata SHIOKAWA (1979-1980)
Seminaire de Théorie des Nombres de Bordeaux
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Iekata SHIOKAWA (1980-1981)
Seminaire de Théorie des Nombres de Bordeaux
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