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POWER-FREE VALUES OF POLYNOMIALS

Abstract:
For irreducible polynomials of the form Xd + c we establish the expected asymptotic formula for the number of k-free integers nd + c with n ≤ x, under the assumption that k ≥ (5d + 3)/9. Previous techniques requiredk> 3d/4.We also prove an entirely analogous result for pd + c with p prime. © 2011. Published by Oxford University Press. All rights reserved.
Publication status:
Published

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Publisher copy:
10.1093/qmath/har030

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
QUARTERLY JOURNAL OF MATHEMATICS
Volume:
64
Issue:
1
Pages:
177-188
Publication date:
2013-03-05
DOI:
EISSN:
1464-3847
ISSN:
0033-5606
URN:
uuid:52bd2330-b36b-4f91-a0cb-e26384b776e6
Source identifiers:
394590
Local pid:
pubs:394590
Language:
English

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