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Smooth Values of Polynomials

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Smooth Values of Polynomials. / Fretwell, Dan; Wooley, Trevor; Bober, Jonathan et al.
In: Journal of the Australian Mathematical Society, Vol. 108, No. 2, 01.04.2020, p. 245-261.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Fretwell, D, Wooley, T, Bober, J & Martin, G 2020, 'Smooth Values of Polynomials', Journal of the Australian Mathematical Society, vol. 108, no. 2, pp. 245-261. https://doi.org/10.1017/s1446788718000320

APA

Fretwell, D., Wooley, T., Bober, J., & Martin, G. (2020). Smooth Values of Polynomials. Journal of the Australian Mathematical Society, 108(2), 245-261. https://doi.org/10.1017/s1446788718000320

Vancouver

Fretwell D, Wooley T, Bober J, Martin G. Smooth Values of Polynomials. Journal of the Australian Mathematical Society. 2020 Apr 1;108(2):245-261. doi: 10.1017/s1446788718000320

Author

Fretwell, Dan ; Wooley, Trevor ; Bober, Jonathan et al. / Smooth Values of Polynomials. In: Journal of the Australian Mathematical Society. 2020 ; Vol. 108, No. 2. pp. 245-261.

Bibtex

@article{f51e1006e6e14590b05a393a64bde766,
title = "Smooth Values of Polynomials",
abstract = "Given f Z[t] of positive degree, we investigate the existence of auxiliary polynomials g Z[t] for which factors as a product of polynomials of small relative degree. One consequence of this work shows that for any quadratic polynomial f Z[t] and any ϵ > 0, there are infinitely many for which the largest prime factor of f(n) is no larger than n.",
keywords = "Smooth numbers, polynomials, small degree irreducible factors",
author = "Dan Fretwell and Trevor Wooley and Jonathan Bober and Greg Martin",
year = "2020",
month = apr,
day = "1",
doi = "10.1017/s1446788718000320",
language = "English",
volume = "108",
pages = "245--261",
journal = "Journal of the Australian Mathematical Society",
issn = "1446-7887",
publisher = "Cambridge University Press",
number = "2",

}

RIS

TY - JOUR

T1 - Smooth Values of Polynomials

AU - Fretwell, Dan

AU - Wooley, Trevor

AU - Bober, Jonathan

AU - Martin, Greg

PY - 2020/4/1

Y1 - 2020/4/1

N2 - Given f Z[t] of positive degree, we investigate the existence of auxiliary polynomials g Z[t] for which factors as a product of polynomials of small relative degree. One consequence of this work shows that for any quadratic polynomial f Z[t] and any ϵ > 0, there are infinitely many for which the largest prime factor of f(n) is no larger than n.

AB - Given f Z[t] of positive degree, we investigate the existence of auxiliary polynomials g Z[t] for which factors as a product of polynomials of small relative degree. One consequence of this work shows that for any quadratic polynomial f Z[t] and any ϵ > 0, there are infinitely many for which the largest prime factor of f(n) is no larger than n.

KW - Smooth numbers

KW - polynomials

KW - small degree irreducible factors

UR - http://dx.doi.org/10.1017/s1446788718000320

U2 - 10.1017/s1446788718000320

DO - 10.1017/s1446788718000320

M3 - Journal article

VL - 108

SP - 245

EP - 261

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 2

ER -