Primitive prime divisors in the critical orbits of one-parameter families of rational polynomials
Abstract For a polynomial $f(x)\in\mathbb{Q}[x]$ and rational numbers c, u, we put $f_c(x)\coloneqq f(x)+c$ , and consider the Zsigmondy set $\calZ(f_c,u)$ associated to the sequence $\{f_c^n(u)-u\}_{n\geq 1}$ , see Definition 1.1, where $f_c^n$ is the n-st iteration of f c . In this paper, we prove that if u is a rational critical point of f, then there exists an M f > 0 such that $\mathbf M_f\geq \max_{c\in \mathbb{Q}}\{\#\calZ(f_c,u)\}$ .
2014 ◽
Vol 17
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pp. 141-158
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1970 ◽
Vol 28
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pp. 278-279
1977 ◽
Vol 35
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pp. 590-591
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1973 ◽
Vol 31
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pp. 472-473
1973 ◽
Vol 31
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pp. 448-449
Macromolecular structures of biological specimens are not obscured by controlled osmium impregnation
1983 ◽
Vol 41
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pp. 606-607
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20 Nm
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1987 ◽
Vol 45
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pp. 954-955