Explicit bounds for composite lacunary polynomials
Let f, g, h∈ ℂ [x] 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 in [9] that there exists a function B1(l) on ℕ, depending only on l and with the property that h(x) can be written as the ratio o...
| Permalink: | http://skupnikatalog.nsk.hr/Record/nsk.NSK01001075564/Details |
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| Matična publikacija: |
Glasnik matematički (Online) 54 (2019), 1 ; str. 11-20 |
| Glavni autor: | Karolus, Christina (Author) |
| Vrsta građe: | e-članak |
| Jezik: | eng |
| Predmet: | |
| Online pristup: |
https://doi.org/10.3336/gm.54.1.02 Glasnik matematički (Online) Hrčak |
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| 008 | 200928s2019 ci |o |0|| ||eng | ||
| 024 | 7 | |2 doi |a 10.3336/gm.54.1.02 | |
| 035 | |a (HR-ZaNSK)001075564 | ||
| 040 | |a HR-ZaNSK |b hrv |c HR-ZaNSK |e ppiak | ||
| 041 | 0 | |a eng |b eng | |
| 042 | |a croatica | ||
| 044 | |a ci |c hr | ||
| 080 | 1 | |a 51 |2 2011 | |
| 100 | 1 | |a Karolus, Christina |4 aut |9 HR-ZaNSK | |
| 245 | 1 | 0 | |a Explicit bounds for composite lacunary polynomials |h [Elektronička građa] / |c Christina Karolus. |
| 500 | |a Bilješke uz tekst. | ||
| 504 | |a Bibliografija: 10 jed. | ||
| 504 | |a Abstract. | ||
| 520 | |a Let f, g, h∈ ℂ [x] 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 in [9] that there exists a function B1(l) on 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 B1(l) terms. Here, we give explicit estimates for this function or, more precisely, we prove that one may take for instance B1(l)=(4l) (2l) (3l) (l+1). Moreover, in the case l=2, a better bound is obtained using the same strategy. | ||
| 653 | 0 | |a Polinomi |a Lakunarni polinomi |a Rastav polinoma |a Reducibilni polinomi |a Faktorizacija polinoma | |
| 773 | 0 | |t Glasnik matematički (Online) |x 1846-7989 |g 54 (2019), 1 ; str. 11-20 |w nsk.(HR-ZaNSK)000659858 | |
| 981 | |b Be2019 |b B05/19 | ||
| 998 | |b tino2010 | ||
| 856 | 4 | 0 | |u https://doi.org/10.3336/gm.54.1.02 |
| 856 | 4 | 0 | |u https://web.math.pmf.unizg.hr/glasnik/EasyTracker.php?id=54102 |y Glasnik matematički (Online) |
| 856 | 4 | 0 | |u https://hrcak.srce.hr/220840 |y Hrčak |
| 856 | 4 | 1 | |y Digitalna.nsk.hr |