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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] Dartyge, C., Mauduit, C., and Sárközy, A., Polynomial values and generators with missing digits in finite fields . Funct. Approx. Comment. Math. 52(2015), 65–74. . Google Scholar | DOI

[2] Dietmann, R., Elsholtz, C., and Shparlinski, I., Prescribing the binary digits of squarefree numbers and quadratic residues . Trans. Amer. Math. Soc. 369(2017), 8369–8388. . Google Scholar | DOI

[3] Ha, J., Irreducible polynomials with several prescribed coefficients . Finite Field Appl. 40(2016), 10–25. . Google Scholar | DOI

[4] Hayes, D. R., The expression of a polynomial as a sum of three irreducibles . Acta Arith. 11(1966), 461–488. . Google Scholar | DOI

[5] Maynard, J., Primes with restricted digits. 2016. arxiv:1604.01041. Google Scholar

[6] Oppenheim, A. and Shusterman, M., Squarefree polynomials with prescribed coefficients . J. Number Theory 187(2018), 189–197. . Google Scholar | DOI

[7] Pollack, P., Irreducible polynomials with several prescribed coefficients . Finite Fields Appl. 22(2013), 70–78. . Google Scholar | DOI

[8] Tuxanidy, A. and Wang, Q., Irreducible polynomials with prescribed sums of coefficients. 2016. arxiv:1605.00351. Google Scholar

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