PreprintCC BY 4.0arXiv
Projective symmetries of Chebyshev polynomials
Abstract
Let k be an algebraically closed field of odd characteristic p, and let φd be the monic Chebyshev polynomial defined by φd(t+t−1)=td+t−d. For d>4 with pnmid d, let Hd≤PGL2(k) be the stabilizer of the zero set of φd. We show that Hd≅ Dd,&if 2d=pr+1 for some integer r≥ 1, S3,&if 4d=pr+1 for some integer r≥ 1, C2,&otherwise.
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BibTeX
@misc{tafazolian2026projective,
title = {{Projective symmetries of Chebyshev polynomials}},
author = {Saeed Tafazolian and Jaap Top},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05096},
eprint = {2611.05096},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05096},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Projective symmetries of Chebyshev polynomials
AU - Saeed Tafazolian
AU - Jaap Top
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05096
UR - https://arxiv.org/abs/2611.05096
AB - Let k be an algebraically closed field of odd characteristic p, and let φ_d be the monic Chebyshev polynomial defined by φ_d(t+t^−1)=t^d+t^−d. For d>4 with pnmid d, let H_d≤PGL_2(k) be the stabilizer of the zero set of φ_d. We show that H_d≅ D_d,&if 2d=p^r+1 for some integer r≥ 1, S_3,&if 4d=p^r+1 for some integer r≥ 1, C_2,&otherwise.
ER -