Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4582666 | Finite Fields and Their Applications | 2016 | 16 Pages |
Abstract
We study the number of irreducible polynomials over FqFq with some coefficients prescribed. Using the technique developed by Bourgain, we show that there is an irreducible polynomial of degree n with r coefficients prescribed in any location when r≤[(1/4−ϵ)n]r≤[(1/4−ϵ)n] for any ϵ>0ϵ>0 and q is large; and when r≤δnr≤δn for some δ>0δ>0 and for any q . The result improves earlier work of Pollack stating that a similar result holds for r≤[(1−ϵ)n].
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Junsoo Ha,