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PreprintCC BY 4.0arXiv

Monogenity of the irreducible factors of (k,t)-Fibonacci and (k,t)-Lucas polynomials

  • Michail Karatarakis
  • Sumandeep Kaur
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Abstract

In this article, we study the monogenity of the number field generated by a root of an irreducible factor of the generalized (k,t)-Fibonacci and (k,t)-Lucas polynomial sequence. We use Dickson polynomials and their connection with cyclotomic fields to prove our main results. As special cases, we recover the monogenity results for the classical Fibonacci and Lucas polynomials and obtain corresponding monogenity results for Chebyshev polynomials of the first and second kinds.

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Cite

BibTeXRIS
BibTeX
@misc{karatarakis2026monogenity,
  title = {{Monogenity of the irreducible factors of $(k,t)$-Fibonacci and $(k,t)$-Lucas polynomials}},
  author = {Michail Karatarakis and Sumandeep Kaur},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38844},
  eprint = {2609.38844},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38844},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Monogenity of the irreducible factors of (k,t)-Fibonacci and (k,t)-Lucas polynomials
AU  - Michail Karatarakis
AU  - Sumandeep Kaur
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.38844
UR  - https://arxiv.org/abs/2609.38844
AB  - In this article, we study the monogenity of the number field generated by a root of an irreducible factor of the generalized (k,t)-Fibonacci and (k,t)-Lucas polynomial sequence. We use Dickson polynomials and their connection with cyclotomic fields to prove our main results. As special cases, we recover the monogenity results for the classical Fibonacci and Lucas polynomials and obtain corresponding monogenity results for Chebyshev polynomials of the first and second kinds.
ER  -