Results 1 to 10 of about 635 (41)

On the Nonexistence of Partial Difference Sets by Projections to Finite Fields

Communications in Mathematical Research, 2022
In the study of (partial) difference sets and their generalizations in groups G, the most widely used method is to translate their definition into an equation over group ring Z[G] and to investigate this equation by applying complex representations of G.
Yue Zhou
semanticscholar   +1 more source

On computing factors of cyclotomic polynomials [PDF]

arXiv.org, 1993
For odd square-free n > 1 the cyclotomic polynomial Φn(x) satisfies the identity of Gauss 4Φn(x) = An − (−1)(n−1)/2nB2 n. A similar identity of Aurifeuille, Le Lasseur and Lucas is Φn((−1)x) = C n − nxD n or, in the case that n is even and square-free ...
Richard P. Brent
semanticscholar   +1 more source

The strong primitive normal basis theorem [PDF]

, 2006
An element α of the extension E of degree n over the finite field F = GF(q) is called free over F if {α, α q , . . . , α q n 1 } is a (normal) basis of E/F.
Stephen D. Cohen, Sophie Huczynska
semanticscholar   +1 more source

Value sets of sparse polynomials [PDF]

, 2018
We obtain a new lower bound on the size of value set f(F_p) of a sparse polynomial f in F_p[X] over a finite field of p elements when p is prime. This bound is uniform with respect of the degree and depends on some natural arithmetic properties of the ...
Shparlinski, Igor E., Voloch, Jose Felipe   +1 more
core   +2 more sources

On the roots of the substitution Dickson polynomials

International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 6, Page 349-353, 2002., 2002
We show that under the composition of multivalued functions, the set of the y‐radical roots of the Dickson substitution polynomial gd(x, a) − gd(y, a) is generated by one of the roots. Hence, we show an expected generalization of the fact that, under the composition of the functions, the y‐radical roots of xd − yd are generated by ζdy.
Javier Gomez-Calderon
wiley   +1 more source

Multi-wavelength observations of Galactic hard X-ray sources discovered by INTEGRAL. I. The nature of the companion star [PDF]

, 2008
Context: The INTEGRAL hard X-ray observatory has revealed an emerging population of highly obscured X-ray binary systems through multi-wavelength observations.
Bird, Bird, Bodaghee, Bodaghee, Bohlin, Bronfman, C. Foellmi, Capitanio, Cardelli, Caron, Chaty, Chernyakova, Corbet, Corbet, Corbet, Corbet, Dean, Dickey, F. Rahoui, Filliatre, Hannikainen, Hannikainen, Hanson, Hill, in 't Zand, J. A. Tomsick, J. Rodriguez, Kennea, Kouveliotou, Kuulkers, Landolt, Lebrun, Levine, Liu, Liu, Lutovinov, Lutovinov, Lutovinov, Malizia, Malizia, Malizia, Markwardt, Masetti, Molkov, Munari, Munari, Negueruela, Negueruela, Nespoli, Patel, Pellizza, Persson, Predehl, R. Walter, Rahoui, Revnivtsev, Revnivtsev, Revnivtsev, Rodriguez, Rodriguez, Rodriguez, Rupen, Russeil, S. Chaty, Sguera, Sguera, Sguera, Smith, Smith, Stephen, Sunyaev, Swank, Thompson, Thompson, Tomsick, Tomsick, Tomsick, Türler, Walter, Walter, Zurita Heras   +80 more
core   +5 more sources

Constructing irreducible polynomials with prescribed level curves over finite fields

International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 4, Page 197-200, 2001., 2001
We use Eisenstein′s irreducibility criterion to prove that there exists an absolutely irreducible polynomial P(X, Y) ∈ GF(q)[X, Y] with coefficients in the finite field GF(q) with q elements, with prescribed level curves Xc : = {(x, y) ∈ GF(q)2 | P(x, y) = c}.
Mihai Caragiu
wiley   +1 more source

On the decomposition of xd + aexe + ⋯+a1x + a0

International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 11, Page 777-781, 2000., 2000
Let K denote a field. A polynomial f(x) ∈ K[x] is said to be decomposable over K if f(x) = g(h(x)) for some polynomials g(x) and h(x) ∈ K[x] with 1 < deg(h) < deg(f). Otherwise f(x) is called indecomposable. If f(x) = g(xm) with m > 1, then f(x) is said to be trivially decomposable.
Javier Gomez-Calderon
wiley   +1 more source

The radical factors of f(x) − f(y) over finite fields

International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 799-802, 1997., 1996
Let F denote the finite field of order q For f(x) in F[x], let f*(x, y) denote the substitution polynomial f(x) − f(y). The polynomial f*(x, y) has frequently been used in questions on the values set of f(x) In this paper we consider the irreducible factors of f*(x, y) that are “solvable by radicals” We show that if R(x, y) denotes the product of all ...
Javier Gomez-Calderon
wiley   +1 more source

It is easy to determine whether a given integer is prime

, 2004
“The problem of distinguishing prime numbers from composite numbers, and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.
A. Granville
semanticscholar   +1 more source