Salomon's Theorem for polynomials with several parameters

Maria Frontczak; Przemysław Skibiński; Stanisław Spodzieja

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The Diophantine equation f(x) = g(y)

Yuri Bilu, Robert Tichy (2000)

Acta Arithmetica

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Approximation exponents for algebraic functions in positive characteristic

Bernard de Mathan (1992)

Acta Arithmetica

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In this paper, we study rational approximations for algebraic functions in characteristic p > 0. We obtain results for elements satisfying an equation of the type $α = (A α^{q} + B) / (C α^{q} + D)$ , where q is a power of p.

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Panagiotis Tzekis, Nicholas Karampetakis, Haralambos Terzidis (2007)

International Journal of Applied Mathematics and Computer Science

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The main contribution of this work is to provide an algorithm for the computation of the GCD of 2-D polynomials, based on DFT techniques. The whole theory is implemented via illustrative examples.

On real polynomials without nonnegative roots.

Brunotte, Horst (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Formulae for the singularities at infinity of plane algebraic curves.

Gwoździewicz, Janusz, Płoski, Arkadiusz (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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On three questions concerning $0, 1$ -polynomials

Michael Filaseta, Carrie Finch, Charles Nicol (2006)

Journal de Théorie des Nombres de Bordeaux

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We answer three reducibility (or irreducibility) questions for $0, 1$ -polynomials, those polynomials which have every coefficient either $0$ or $1$ . The first concerns whether a naturally occurring sequence of reducible polynomials is finite. The second is whether every nonempty finite subset of an infinite set of positive integers can be the set of positive exponents of a reducible $0, 1$ -polynomial. The third is the analogous question for exponents of irreducible $0, 1$ -polynomials.

The growth of regular functions on algebraic sets

A. Strzeboński (1991)

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We are concerned with the set of all growth exponents of regular functions on an algebraic subset V of $ℂ^{n}$ . We show that its elements form an increasing sequence of rational numbers and we study the dependence of its structure on the geometric properties of V.