Geodesic
Irreducible Polynomials Over a Finite Field with Restricted Coefficients
Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 429-439

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DOI

We prove a function field analogue of Maynard’s celebrated result about primes with restricted digits. That is, for certain ranges of parameters $n$ and $q$, we prove an asymptotic formula for the number of irreducible polynomials of degree $n$ over a finite field $\mathbb{F}_{q}$ whose coefficients are restricted to lie in a given subset of $\mathbb{F}_{q}$.
DOI : 10.4153/CMB-2018-027-x
Mots-clés : finite field, irreducible polynomial, restricted coefficients 
Porritt, Sam. Irreducible Polynomials Over a Finite Field with Restricted Coefficients. Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 429-439. doi: 10.4153/CMB-2018-027-x
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     author = {Porritt, Sam},
     title = {Irreducible {Polynomials} {Over} a {Finite} {Field} with {Restricted} {Coefficients}},
     journal = {Canadian mathematical bulletin},
     pages = {429--439},
     year = {2019},
     volume = {62},
     number = {2},
     doi = {10.4153/CMB-2018-027-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-027-x/}
}
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