Fedor Petrov (2014)
Acta Arithmetica
Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of |f(A,B)| for finite subsets A, B of a field, and a polynomial f(x,y) of the form f(x,y) = g(x) + yh(x), where the degree of g is greater than that of h.
F. Halter-Koch, W. Narkiewicz (1992)
Monatshefte für Mathematik
Zimmermann, Karl (2007)
The New York Journal of Mathematics [electronic only]
Konrad J. Heuvers, Pal Fischer (1987)
Aequationes mathematicae
Clemens Fuchs, Umberto Zannier (2012)
Journal of the European Mathematical Society
We consider a rational function which is ‘lacunary’ in the sense that it can be expressed as the ratio of two polynomials (not necessarily coprime) having each at most a given number of terms. Then we look at the possible decompositions , where are rational functions of degree larger than 1. We prove that, apart from certain exceptional cases which we completely describe, the degree of is bounded only in terms of (and we provide explicit bounds). This supports and quantifies the intuitive...
Mohamed Ayad, Donald L. McQuillan (2001)
Acta Arithmetica
A. Białynicki-Birula, A. Schinzel (2011)
Colloquium Mathematicae
Kurt Girstmair (2003)
Acta Arithmetica
T. Pezda (1994)
Colloquium Mathematicae
T. Pezda (1996)
Colloquium Mathematicae
Martine Pathiaux (1971/1972)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
M. Sopmann (1924)
Mathematische Annalen
Martin Kneser (1981)
Mathematische Zeitschrift
Andrzej Schinzel (1995)
Acta Arithmetica
W. Boutabaa, William Cherry, Alain Escassut (2002)
Acta Arithmetica
Antonia W. Bluher (2004)
Acta Arithmetica
Andrzej Białynicki-Birula, Andrzej Schinzel (2010)
Acta Arithmetica
Sadeghi, Jafar (2009)
APPS. Applied Sciences
Andrzej Schinzel (1982)
Acta Arithmetica
R. Dvornicich, U. Zannier (1994)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze