Smooth values of polynomials

Jonathan Bober; Dan Fretwell; Greg Martin; Trevor Wooley

doi:10.1017/S1446788718000320

Smooth values of polynomials

Jonathan Bober
, Dan Fretwell
, Greg Martin
, Trevor Wooley

Research output: Contribution to journal › Article (Academic Journal) › peer-review

6 Citations (Scopus)

329 Downloads (Pure)

Abstract

Given of positive degree, we investigate the existence of auxiliary polynomials for which factors as a product of polynomials of small relative degree. One consequence of this work shows that for any quadratic polynomial and any 0$]]>, there are infinitely many for which the largest prime factor of is no larger than.

Original language	English
Pages (from-to)	245-261
Number of pages	17
Journal	Journal of the Australian Mathematical Society
Volume	108
Issue number	2
Early online date	1 Feb 2019
DOIs	https://doi.org/10.1017/S1446788718000320
Publication status	E-pub ahead of print - 1 Feb 2019

Keywords

Smooth numbers
polynomials
small degree irreducible factors

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10.1017/S1446788718000320

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Cambridge University Press at https://www.cambridge.org/core/journals/journal-of-the-australian-mathematical-society/article/smooth-values-of-polynomials/C7323675DFBAFA2489F47C9BC0B7EB83 . Please refer to any applicable terms of use of the publisher.
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@article{72e240a278d34731aa81b827d7941b78,

title = "Smooth values of polynomials",

abstract = "Given of positive degree, we investigate the existence of auxiliary polynomials for which factors as a product of polynomials of small relative degree. One consequence of this work shows that for any quadratic polynomial and any 0\$]]>, there are infinitely many for which the largest prime factor of is no larger than.",

keywords = "Smooth numbers, polynomials, small degree irreducible factors",

author = "Jonathan Bober and Dan Fretwell and Greg Martin and Trevor Wooley",

year = "2019",

month = feb,

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",

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TY - JOUR

T1 - Smooth values of polynomials

AU - Bober, Jonathan

AU - Fretwell, Dan

AU - Martin, Greg

AU - Wooley, Trevor

PY - 2019/2/1

Y1 - 2019/2/1

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

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

KW - Smooth numbers

KW - polynomials

KW - small degree irreducible factors

UR - https://arxiv.org/abs/1710.01970

UR - https://www.scopus.com/pages/publications/85061012956

U2 - 10.1017/S1446788718000320

DO - 10.1017/S1446788718000320

M3 - Article (Academic Journal)

SN - 1446-7887

VL - 108

SP - 245

EP - 261

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 2

ER -

Smooth values of polynomials

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Dr Jonathan W Bober

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Smooth values of polynomials

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Dr Jonathan W Bober

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