This paper completely settles a conjecture of Schinzel (formulated already by Erdos in a special case) stating that if a composite polynomial g(h(x)) has at most L terms then already h(x) must have at most t_L terms, where t_L is a function of L only. This actually sharpens the original Schinzel's conjecture. The methods are completely new and also yield an algorithm for "writing down" the possible composition factors of a general polynomial with a given number of terms.

On composite lacunary polynomials and the proof of a conjecture of Schinzel

ZANNIER, UMBERTO
2008

Abstract

This paper completely settles a conjecture of Schinzel (formulated already by Erdos in a special case) stating that if a composite polynomial g(h(x)) has at most L terms then already h(x) must have at most t_L terms, where t_L is a function of L only. This actually sharpens the original Schinzel's conjecture. The methods are completely new and also yield an algorithm for "writing down" the possible composition factors of a general polynomial with a given number of terms.
2008
Polynomials; Complexity
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/4957
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