Square-free smooth polynomials in residue classes and generators of irreducible polynomials
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- by Christian Bagshaw;
- Proc. Amer. Math. Soc. 151 (2023), 1017-1029
- DOI: https://doi.org/10.1090/proc/16201
- Published electronically: December 21, 2022
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Abstract:
Building upon the work of A. Booker and C. Pomerance [Proc. Amer. Math. Soc. 145 (2017), pp. 5035–5042], we prove that for a prime power $q \geq 7$, every residue class modulo an irreducible polynomial $F \in \mathbb {F}_q[X]$ has a non-constant, square-free representative which has no irreducible factors of degree exceeding $\deg F -1$. We also give applications to generating sequences of irreducible polynomials.References
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Bibliographic Information
- Christian Bagshaw
- Affiliation: School of Mathematics and Statistics, University of New South Wales. Sydney, NSW 2052, Australia
- MR Author ID: 1503105
- Email: c.bagshaw@unsw.edu.au
- Received by editor(s): February 7, 2022
- Received by editor(s) in revised form: June 5, 2022, and June 14, 2022
- Published electronically: December 21, 2022
- Additional Notes: During the preparation of this work, the author was supported by an Australian Government Research Training Program (RTP) Scholarship.
- Communicated by: Amanda Folsom
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 1017-1029
- MSC (2020): Primary 11T06, 11T24
- DOI: https://doi.org/10.1090/proc/16201
- MathSciNet review: 4531635