Results 191 to 200 of about 12,236 (229)

CYCLOTOMIC AND INVERSE CYCLOTOMIC POLYNOMIAL

Advances in Mathematics: Scientific Journal, 2022
In this article, the companion matrix of the cyclotomic and inverse cyclotomic polynomial is found. To determine the flat, gap, jump of the $\Phi_{n}(x)$ and $\Psi_{n}(x)$ for the binary, ternary, quaternary, quinary cyclotomic polynomial. To find some properties of the cyclotomic and inverse cyclotomic polynomial.
D. Nagarajan, A. Rameshkumar
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Cyclotomic polynomial factors

The Mathematical Gazette, 2005
The n th roots of unity play a key role in abstract algebra, providing a rich link between groups, vectors, regular n -gons, and algebraic factorizations. This richness permits extensive study. A historical example of this interest is the 1938 challenge
Richard Grassl, Tabitha T.Y. Mingus
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Exploring cyclotomic polynomials

The Mathematical Gazette, 2001
Cyclotomic polynomials, ( x p - l)/( x -1), have ( p -1) zeros exp(2πi q
D. G. C. Mckeon, T. N. Sherry
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CYCLOTOMIC FACTORS OF BORWEIN POLYNOMIALS

Bulletin of the Australian Mathematical Society, 2019
A cyclotomic polynomial $\unicode[STIX]{x1D6F7}_{k}(x)$ is an essential cyclotomic factor of $f(x)\in \mathbb{Z}[x]$ if $\unicode[STIX]{x1D6F7}_{k}(x)\mid f(x)$ and every prime divisor of $k$ is less than or equal to the number of terms of $f.$ We show that if a monic polynomial with coefficients from $\{-1,0,1\}$ has a cyclotomic factor, then it has ...
BISWAJIT KOLEY, SATYANARAYANA REDDY ARIKATLA   +1 more
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INFINITE PRODUCTS OF CYCLOTOMIC POLYNOMIALS

Bulletin of the Australian Mathematical Society, 2015
We study analytic properties of certain infinite products of cyclotomic polynomials that generalise some products introduced by Mahler. We characterise those that have the unit circle as a natural boundary and use associated Dirichlet series to obtain their asymptotic behaviour near roots of unity.
Duke, William, Nguyen, Ha Nam
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Quasi-Cyclotomic Polynomials

The American Mathematical Monthly, 1932
(1932). Quasi-Cyclotomic Polynomials. The American Mathematical Monthly: Vol. 39, No. 7, pp. 383-389.
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Resultants of cyclotomic polynomials

Publicationes Mathematicae Debrecen, 1997
A simple proof is given for a result of \textit{T. M. Apostol} [Proc. Am. Math. Soc. 24, 457-462 (1970; Zbl 0188.34002)] and \textit{F. E. Diederichsen} [Abh. Math. Semin. Univ. Hamb. 13, 357-412 (1940; Zbl 0023.01302)] concerning resultants of cyclotomic polynomials.
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On values of cyclotomic polynomials. V.

2016
Summary: In this paper, using properties of cyclotomic polynomial, we give a new proof on some fundamental results in finite fields, a new method of factorization of a number, and a suggestion about new cyclic codes. Part IV, cf. Bull. Fac. Sci. Technol., Hirosaki Univ. 1, No. 1, 1--7 (1998; Zbl 0922.11104).
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Some q-Supercongruences Modulo the Fifth Power of a Cyclotomic Polynomial from Squares of q-Hypergeometric Series

Results in Mathematics, 2021
Chun Wang
exaly  

Products of Cyclotomic Polynomials

2002
As in Chapter 3, the nth cyclotomic polynomial Φ n is the minimal polynomial of a primitive nth root of unity. Recall that Φ n is given by $$ {\Phi_n}(z) = \prod\limits_{{\begin{array}{*{20}{c}} {1 \leqslant j \leqslant n} \\ {\gcd \left( {j,n} \right) = 1} \\ \end{array} }} {\left( {z - \exp \left( {{{{j2\pi i}} \left/ {n} \right.}} \right ...
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