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- W2607281041 abstract "Let $f, g, hin mathbb{C}left[xright]$ be non-constant complex polynomials satisfying $f(x)=g(h(x))$ and let $f$ be lacunary in the sense that it has at most $l$ non-constant terms. Zannier proved that there exists a function $B_1(l)$ on $mathbb{N}$, depending only on $l$ and with the property that $h(x)$ can be written as the ratio of two polynomials having each at most $B_1(l)$ terms. Here, we give explicit estimates for this function or, more precicely, we prove that one may take for instance [B_1(l)=(4l)^{(2l)^{(3l)^{l+1}}}.] Moreover, in the case $l=2$, a better result is obtained using the same strategy." @default.
- W2607281041 created "2017-04-28" @default.
- W2607281041 creator A5008739257 @default.
- W2607281041 date "2017-04-13" @default.
- W2607281041 modified "2023-09-27" @default.
- W2607281041 title "Explicit bounds for composite lacunary polynomials" @default.
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