Polynomials with integer coefficients and Chebyshev polynomials

2017 ◽  
Vol 222 (6) ◽  
pp. 797-818
Author(s):  
Roal′d M. Trigub
Keyword(s):  
Chebyshev Polynomials ◽  
Integer Coefficients

scholarly journals Regular polygons, Morgan-Voyce polynomials, and Chebyshev polynomials

2021 ◽  
Vol 27 (2) ◽  
pp. 79-87
Author(s):  
Jorma K. Merikoski ◽  
Keyword(s):  
Chebyshev Polynomials ◽  
Monic Polynomial ◽  
Regular Polygons ◽  
Integer Coefficients

We say that a monic polynomial with integer coefficients is a polygomial if its each zero is obtained by squaring the edge or a diagonal of a regular n-gon with unit circumradius. We find connections of certain polygomials with Morgan-Voyce polynomials and further with Chebyshev polynomials of second kind.

Chebyshev Polynomials and Integer Coefficients

2019 ◽  
Vol 105 (1-2) ◽  
pp. 291-300
Author(s):  
R. M. Trigub
Keyword(s):  
Chebyshev Polynomials ◽  
Integer Coefficients

The Total Character of a Finite Group

2015 ◽  
Vol 22 (spec01) ◽  
pp. 775-788
Author(s):  
Stephen Humphries ◽  
Chelsea Kennedy ◽  
Emma Rode
Keyword(s):  
Finite Group ◽  
Chebyshev Polynomials ◽  
Irreducible Character ◽  
Character Group ◽  
Irreducible Characters ◽  
Integer Coefficients ◽  
A Finite Group

The total character τ(G) of a finite group G is the sum of the irreducible characters of G. We present conditions under which τ(G) can be written as a polynomial with integer coefficients in an irreducible character of G. Such a group we call a total character group. We show that the dicyclic group of order 4n is a total character group if and only if n ≡ 2, 3 mod 4. The polynomial used is a sum of Chebyshev polynomials of the second kind. We also show that Sn (n ≥ 4) is not a total character group.

scholarly journals Total characters and Chebyshev polynomials

2003 ◽  
Vol 2003 (38) ◽  
pp. 2447-2453 ◽  
Author(s):  
Eirini Poimenidou ◽  
Homer Wolfe
Keyword(s):  
Finite Group ◽  
Chebyshev Polynomials ◽  
Irreducible Character ◽  
Dihedral Group ◽  
Dihedral Groups ◽  
Irreducible Characters ◽  
Integer Coefficients ◽  
Complete Answer ◽  
A Finite Group

The total characterτof a finite groupGis defined as the sum of all the irreducible characters ofG. K. W. Johnson asks when it is possible to expressτas a polynomial with integer coefficients in a single irreducible character. In this paper, we give a complete answer to Johnson's question for all finite dihedral groups. In particular, we show that, when such a polynomial exists, it is unique and it is the sum of certain Chebyshev polynomials of the first kind in any faithful irreducible character of the dihedral groupG.

On the Security of Public-Key Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$

2010 ◽  
Vol 59 (10) ◽  
pp. 1392-1401 ◽  
Author(s):  
Xiaofeng Liao ◽  
Fei Chen ◽  
Kwok-wo Wong
Keyword(s):  
Finite Field ◽  
Chebyshev Polynomials ◽  
Public Key

scholarly journals New Specific and General Linearization Formulas of Some Classes of Jacobi Polynomials

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 74
Author(s):  
Waleed Mohamed Abd-Elhameed ◽  
Afnan Ali
Keyword(s):  
Chebyshev Polynomials ◽  
Hypergeometric Functions ◽  
Jacobi Polynomials ◽  
Algebraic Computation ◽  
Ultraspherical Polynomials ◽  
Current Article ◽  
Linearization Coefficients

The main purpose of the current article is to develop new specific and general linearization formulas of some classes of Jacobi polynomials. The basic idea behind the derivation of these formulas is based on reducing the linearization coefficients which are represented in terms of the Kampé de Fériet function for some particular choices of the involved parameters. In some cases, the required reduction is performed with the aid of some standard reduction formulas for certain hypergeometric functions of unit argument, while, in other cases, the reduction cannot be done via standard formulas, so we resort to certain symbolic algebraic computation, and specifically the algorithms of Zeilberger, Petkovsek, and van Hoeij. Some new linearization formulas of ultraspherical polynomials and third-and fourth-kinds Chebyshev polynomials are established.

Irreducibility Results for Compositions of Polynomials with Integer Coefficients

2006 ◽  
Vol 149 (1) ◽  
pp. 31-41 ◽  
Author(s):  
Anca Iuliana Bonciocat ◽  
Alexandru Zaharescu
Keyword(s):  
Integer Coefficients
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