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Search: MSC category 12E10 ( Special polynomials )

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1. CMB Online first

Yamagishi, Masakazu
Resultants of Chebyshev Polynomials: The First, Second, Third, and Fourth Kinds
We give an explicit formula for the resultant of Chebyshev polynomials of the first, second, third, and fourth kinds. We also compute the resultant of modified cyclotomic polynomials.

Keywords:resultant, Chebyshev polynomial, cyclotomic polynomial
Categories:11R09, 11R18, 12E10, 33C45

2. CMB 2007 (vol 50 pp. 313)

Tzermias, Pavlos
On Cauchy--Liouville--Mirimanoff Polynomials
Let $p$ be a prime greater than or equal to 17 and congruent to 2 modulo 3. We use results of Beukers and Helou on Cauchy--Liouville--Mirimanoff polynomials to show that the intersection of the Fermat curve of degree $p$ with the line $X+Y=Z$ in the projective plane contains no algebraic points of degree $d$ with $3 \leq d \leq 11$. We prove a result on the roots of these polynomials and show that, experimentally, they seem to satisfy the conditions of a mild extension of an irreducibility theorem of P\'{o}lya and Szeg\"{o}. These conditions are \emph{conjecturally} also necessary for irreducibility.

Categories:11G30, 11R09, 12D05, 12E10

3. CMB 2006 (vol 49 pp. 113)

Ledet, Arne
$\PSL(2,2^n)$-Extensions Over $\mathbb F_{2^n}$
We construct a one-parameter generic polynomial for $\PSL(2,2^n)$ over $\mathbb F_{2^n}$.

Categories:12F12, 12E10

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