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EnglishThis 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.
http://hdl.handle.net/11384/4957| Titolo: | On composite lacunary polynomials and the proof of a conjecture of Schinzel |
| Autori interni: | ZANNIER, UMBERTO |
| Data di pubblicazione: | 2008 |
| Rivista: | INVENTIONES MATHEMATICAE |
| 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. |
| Handle: | http://hdl.handle.net/11384/4957 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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