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Distribution of constant terms of irreducible polynomials in Zp[x]

2019
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Notes on Number Theory and Discrete Mathematics
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We obtain explicit formulas for the number of monic irreducible polynomials with prescribed constant term and degree q k over a finite field. These formulas are derived from work done by Yucas. We show that the number of polynomials of a given constant term depends only on whether the constant term is a residue in the underlying field. We further show that as k becomes large, the proportion of irreducible polynomials having each constant term is asymptotically equal.

doi:10.7546/nntdm.2019.25.4.72-82
fatcat:fnm3tkr6enfrhisznjhx2xpp3a