Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curves defined by Chebyshev polynomials   Working over a field $\kk$ of characteristic zero, this paper studies line
embeddings of the form $\phi = (T_i,T_j,T_k):\A^1\to\A^3$, where $T_n$ denotes
the degree $n$ Chebyshev polynomial of the first kind. In {\it Section 4}, it
is shown that (1) $\phi$ 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.

31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con