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Sequences of consecutive smooth polynomials over a finite field

Authors:	Ariane Masuda Daniel Panario

Institution:	School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6 ; School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6

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 $\ln\ln\ln n$ .

Keywords:	Smooth polynomials finite fields sequences of polynomials

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