On the values of a class of analytic functions at algebraic points
Boris Adamczewski, Yann Bugeaud, Florian Luca (2008)
Acta Arithmetica
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Boris Adamczewski, Yann Bugeaud, Florian Luca (2008)
Acta Arithmetica
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J. Garza, M. I. M. Ishak, C. Pinner (2010)
Acta Arithmetica
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K. Orlov, B. Savić (1983)
Matematički Vesnik
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Tasoev, B.G. (2001)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Hidekazu Tanaka (2009)
Acta Arithmetica
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Paulius Drungilas, Artūras Dubickas (2003)
Colloquium Mathematicae
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We show that the set obtained by adding all sufficiently large integers to a fixed quadratic algebraic number is multiplicatively dependent. So also is the set obtained by adding rational numbers to a fixed cubic algebraic number. Similar questions for algebraic numbers of higher degrees are also raised. These are related to the Prouhet-Tarry-Escott type problems and can be applied to the zero-distribution and universality of some zeta-functions.
J. Wójcik (1975)
Acta Arithmetica
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J. C. Varlet (1975)
Colloquium Mathematicae
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R. Stora (1986)
Recherche Coopérative sur Programme n°25
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Yasushige Watase (2016)
Formalized Mathematics
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This article provides definitions and examples upon an integral element of unital commutative rings. An algebraic number is also treated as consequence of a concept of “integral”. Definitions for an integral closure, an algebraic integer and a transcendental numbers [14], [1], [10] and [7] are included as well. As an application of an algebraic number, this article includes a formal proof of a ring extension of rational number field ℚ induced by substitution of an algebraic number to...
Thomas Jarrett
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J. Bochnak, M. Buchner, W. Kucharz (1997)
Annales Polonici Mathematici
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We give a criterion for a real-analytic function defined on a compact nonsingular real algebraic set to be analytically equivalent to a rational function.
J. Schmidt (1964)
Colloquium Mathematicae
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Smirnov, A.L. (2004)
Zapiski Nauchnykh Seminarov POMI
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Ludwig Bröcker (2005)
Annales Polonici Mathematici
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Let R be a real closed field with a real valuation v. A ℤ-valued semialgebraic function on Rⁿ is called algebraic if it can be written as the sign of a symmetric bilinear form over R[X₁,. .., Xₙ]. We show that the reduction of such a function with respect to v is again algebraic on the residue field. This implies a corresponding result for limits of algebraic functions in definable families.
Stéphane Fischler (2001)
Acta Arithmetica
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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....
Charles James Hargreave
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