Kapetanakis, Georgios (2017) Prescribing coefficients of invariant irreducible polynomials. Journal of Number Theory, 180 . pp. 615-628. ISSN 0022-314X (Print) 1096-1658 (Online)
This is the latest version of this item.
Official URL: https://dx.doi.org/10.1016/j.jnt.2017.05.003
Abstract
Let Fq be the finite field of q elements. We define an action of PGL(2,q) on Fq[X] and study the distribution of the irreducible polynomials that remain invariant under this action for lower-triangular matrices. As a result, we describe the possible values of the coefficients of such polynomials and prove that, with a small finite number of possible exceptions, there exist polynomials of given degree with prescribed high-degree coefficients.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Character sums; Finite fields; Hansen–Mullen conjecture |
| Divisions: | Faculty of Engineering and Natural Sciences |
| Depositing User: | Georgios Kapetanakis |
| Date Deposited: | 11 Nov 2026 13:45 |
| Last Modified: | 11 Nov 2026 13:45 |
| URI: | https://research.sabanciuniv.edu/id/eprint/55383 |
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Prescribing coefficients of invariant irreducible polynomials. (deposited 16 Aug 2017 11:29)
- Prescribing coefficients of invariant irreducible polynomials. (deposited 11 Nov 2026 13:45) [Currently Displayed]
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