On coefficients of Carlitz cyclotomic polynomials
| dc.contributor.author | Bamunoba, Alex Samuel | |
| dc.date.accessioned | 2026-03-05T10:17:43Z | |
| dc.date.issued | 2016 | |
| dc.description.abstract | Let n ∈Z+, and Φn(x)be the nth classical cyclotomic polynomial. In [4, Theorem1], D. Lehmer showed that the geometric mean of {Φs(1) :s, n ∈Z+, s ≤n} →e ≈2.71828, as n →∞. Replacing Zby Fq[T], and the nth elementary cylcotomic polynomial Φn(x)by the Carlitz m-cyclotomic polynomial Φm(x), where m ∈Fq[T], we obtain an analogue to Lehmer’s result. We also express Φm(0) ∈F2[T]in terms of φ∗(•), the Pillai polynomial function. The resulting expression is a function field analogue of Hölder’s formula for Φn(1). | |
| dc.description.sponsorship | This work was carried out with financial support from the Stellenbosch Postgraduate Merit Bursary Scheme and the government of Canada’s International Development Research Centre (IDRC) grant number SAMUG2009004S, and within the framework of the AIMS Research for Africa Project. | |
| dc.identifier.citation | Bamunoba, A. S. (2016). On coefficients of Carlitz cyclotomic polynomials. Finite Fields and Their Applications, 37, 28–35. https://doi.org/10.1016/j.ffa.2015.08.006 | |
| dc.identifier.uri | https://ir.lirauni.ac.ug/handle/123456789/1051 | |
| dc.language.iso | en | |
| dc.publisher | Finite Fields and Their Applications | |
| dc.subject | Carlitz polynomials Carlitz cyclotomic polynomials Pillai function | |
| dc.title | On coefficients of Carlitz cyclotomic polynomials | |
| dc.type | Article |