Sequences of consecutive smooth polynomials over a finite field

Masuda, Ariane; Panario, Daniel

doi:10.1090/S0002-9939-06-08611-4

Sequences of consecutive smooth polynomials over a finite field
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by Ariane Masuda and Daniel Panario PDF

Proc. Amer. Math. Soc. 135 (2007), 1271-1277 Request permission

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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