Uniformization of a class of algebraic functions of the third degree by the method of differential equations
J. Janikowski (1967)
Colloquium Mathematicae
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J. Janikowski (1967)
Colloquium Mathematicae
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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....
P. Cijsouw, R. Tijdeman (1973)
Acta Arithmetica
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J. Wójcik (1975)
Acta Arithmetica
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Fabrizio Barroero (2015)
Acta Arithmetica
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Let k be a number field and S a finite set of places of k containing the archimedean ones. We count the number of algebraic points of bounded height whose coordinates lie in the ring of S-integers of k. Moreover, we give an asymptotic formula for the number of S̅-integers of bounded height and fixed degree over k, where S̅ is the set of places of k̅ lying above the ones in S.
J. Garza, M. I. M. Ishak, C. Pinner (2010)
Acta Arithmetica
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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...
Hajime Kaneko (2012)
Acta Arithmetica
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Henryk Żołądek (1995)
Studia Mathematica
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We give a new proof of Jouanolou’s theorem about non-existence of algebraic solutions to the system . We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.
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.
K. Orlov, B. Savić (1983)
Matematički Vesnik
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J. C. Varlet (1975)
Colloquium Mathematicae
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Thomas Jarrett
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Mamoru Takeuchi (2005)
Acta Arithmetica
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Robert M. Fossum (1980)
Publications mathématiques et informatique de Rennes
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J. Schmidt (1964)
Colloquium Mathematicae
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