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Irreducible Polynomials Over a Finite Field with Restricted Coefficients
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 62 / Issue 2 / June 2019
- Published online by Cambridge University Press:
- 07 January 2019, pp. 429-439
- Print publication:
- June 2019
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- Article
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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 
$\mathbb{F}_{q}$.
