A Goldbach theorem for polynomials of low degree over odd finite fields
Page 1 Next
Gove Effinger (1983)
Acta Arithmetica
David Naccache de Paz, Halim M'Silti (1990)
RAIRO - Operations Research - Recherche Opérationnelle
Le Anh Vinh, Dang Phuong Dung (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Halbeisen, L. (2005)
Acta Mathematica Universitatis Comenianae. New Series
David A. Clark (1994)
Manuscripta mathematica
Ahuja, Mangho, Bruening, James (1999)
Bulletin of the Malaysian Mathematical Society. Second Series
Lascoux, Alain (2001)
The Electronic Journal of Combinatorics [electronic only]
Ovall, Jeffrey S. (2004)
ELA. The Electronic Journal of Linear Algebra [electronic only]
J. Loxton, Alfred van der Poorten (1987)
Acta Arithmetica
Zítko, Jan, Kuřátko, Jan (2010)
Programs and Algorithms of Numerical Mathematics
The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid’s algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using - transformation and -factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.
Haukkanen, Pentti (2006)
Journal of Inequalities and Applications [electronic only]
Eliaš, Ján, Zítko, Jan (2013)
Programs and Algorithms of Numerical Mathematics
The computation of polynomial greatest common divisor (GCD) ranks among basic algebraic problems with many applications, for example, in image processing and control theory. The problem of the GCD computing of two exact polynomials is well defined and can be solved symbolically, for example, by the oldest and commonly used Euclid’s algorithm. However, this is an ill-posed problem, particularly when some unknown noise is applied to the polynomial coefficients. Hence, new methods for the GCD computation...
Sudhir R. Ghorpade, Samrith Ram (2012)
Acta Arithmetica
William D. Banks, Igor E. Shparlinski (2004)
Acta Arithmetica
Zítko, Jan, Eliaš, Ján (2013)
Programs and Algorithms of Numerical Mathematics
The coefficients of the greatest common divisor of two polynomials and (GCD) can be obtained from the Sylvester subresultant matrix transformed to lower triangular form, where and deg(GCD) needs to be computed. Firstly, it is supposed that the coefficients of polynomials are given exactly. Transformations of for an arbitrary allowable are in details described and an algorithm for the calculation of the GCD is formulated. If inexact polynomials are given, then an approximate greatest...
Agostino Lampariello (1951)
Bollettino dell'Unione Matematica Italiana
Eckstein, Jiří, Zítko, Jan (2015)
Programs and Algorithms of Numerical Mathematics
The computation of the greatest common divisor (GCD) has many applications in several disciplines including computer graphics, image deblurring problem or computing multiple roots of inexact polynomials. In this paper, Sylvester and Bézout matrices are considered for this purpose. The computation is divided into three stages. A rank revealing method is shortly mentioned in the first one and then the algorithms for calculation of an approximation of GCD are formulated. In the final stage the coefficients...
Jack Lamoreaux, Andrew Pollington (1986)
Acta Arithmetica
Christoph Aistleitner, István Berkes, Kristian Seip, Michel Weber (2015)
Acta Arithmetica
We establish a connection between the L² norm of sums of dilated functions whose jth Fourier coefficients are for some α ∈ (1/2,1), and the spectral norms of certain greatest common divisor (GCD) matrices. Utilizing recent bounds for these spectral norms, we obtain sharp conditions for the convergence in L² and for the almost everywhere convergence of series of dilated functions.
Watcharapon Pimsert, Teerapat Srichan, Pinthira Tangsupphathawat (2023)
Czechoslovak Mathematical Journal
We use the estimation of the number of integers such that belongs to an arithmetic progression to study the coprimality of integers in , , .
Page 1 Next