Curves defined by Chebyshev polynomials
| dc.creator | Freudenburg, Gene | |
| dc.creator | Freudenburg, Jenna | |
| dc.date | 2009-02-19 | |
| dc.date.accessioned | 2026-07-07T12:44:14Z | |
| dc.date.available | 2026-07-07T12:44:14Z | |
| dc.description | Working over a field $\kk$ of characteristic zero, this paper studies line embeddings of the form $ϕ= (T_i,T_j,T_k):\A^1\to\A^3$, where $T_n$ denotes the degree $n$ Chebyshev polynomial of the first kind. In {\it Section 4}, it is shown that (1) $ϕ$ is an embedding if and only if the pairwise greatest common divisor of $i,j,k$ is 1, and (2) for a fixed pair $i,j$ of relatively prime positive integers, the embeddings of the form $(T_i,T_j,T_k)$ represent a finite number of algebraic equivalence classes. {\it Section 2} gives an algebraic definition of the Chebyshev polynomials, where their basic identities are established, and {\it Section 3} studies the plane curves $(T_i,T_j)$. {\it Section 5} establishes the Parity Property for Nodal Curves, and uses this to parametrize the family of alternating $(i,j)$-knots over the real numbers. | |
| dc.description | 19 pages, 5 figures, 3 tables | |
| dc.identifier | https://arxiv.org/abs/0902.3440 | |
| dc.identifier | http://arxiv.org/abs/0902.3440 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/220696 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14R10; 14H50; 57M25 | |
| dc.title | Curves defined by Chebyshev polynomials | |
| dc.type | text |