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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sequences of consecutive smooth polynomials over a finite field


Authors: Ariane Masuda and Daniel Panario
Journal: Proc. Amer. Math. Soc. 135 (2007), 1271-1277
MSC (2000): Primary 11T06, 11T99
Published electronically: November 13, 2006
MathSciNet review: 2276634
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Abstract: Given $ \varepsilon > 0$, we show that there are infinitely many sequences of consecutive $ \varepsilon n$-smooth polynomials over a finite field. The number of polynomials in each sequence is approximately $ \ln\ln\ln n$.


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Additional Information

Ariane Masuda
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Email: ariane@math.carleton.ca

Daniel Panario
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Email: daniel@math.carleton.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08611-4
PII: S 0002-9939(06)08611-4
Keywords: Smooth polynomials, finite fields, sequences of polynomials
Received by editor(s): January 19, 2005
Received by editor(s) in revised form: December 14, 2005
Published electronically: November 13, 2006
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.