共查询到20条相似文献,搜索用时 15 毫秒
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S. Ugolini 《Discrete Mathematics》2013,313(22):2656-2662
In this paper we construct an infinite sequence of binary irreducible polynomials starting from any irreducible polynomial . If is of degree , where is odd and is a nonnegative integer, after an initial finite sequence of polynomials , with , the degree of is twice the degree of for any . 相似文献
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We continue our study on counting irreducible polynomials over a finite field with prescribed coefficients. We set up a general combinatorial framework using generating functions with coefficients from a group algebra which is generated by equivalence classes of polynomials with prescribed coefficients. Simplified expressions are derived for some special cases. Our results extend some earlier results. 相似文献
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In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following
theorem:
$
\pi (x) = \frac{q}
{{q - 1}}\frac{x}
{{\log _q x}} + \frac{q}
{{(q - 1)^2 }}\frac{x}
{{\log _q^2 x}} + O\left( {\frac{x}
{{\log _q^3 x}}} \right),x = q^n \to \infty
$
\pi (x) = \frac{q}
{{q - 1}}\frac{x}
{{\log _q x}} + \frac{q}
{{(q - 1)^2 }}\frac{x}
{{\log _q^2 x}} + O\left( {\frac{x}
{{\log _q^3 x}}} \right),x = q^n \to \infty
相似文献
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In this paper, as an analogue of the integer case, we define congruence preserving functions over the residue class rings of polynomials over finite fields. We establish a counting formula for such congruence preserving functions, determine a necessary and sufficient condition under which all congruence preserving functions are also polynomial functions, and characterize such functions. 相似文献
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Daqing Wan. 《Mathematics of Computation》1997,66(219):1195-1212
Weil's character sum estimate is used to study the problem of constructing generators for the multiplicative group of a finite field. An application to the distribution of irreducible polynomials is given, which confirms an asymptotic version of a conjecture of Hansen-Mullen.
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Cemile Tosun 《Discrete Mathematics》2019,342(12):111618
In this paper, we derive explicit factorizations of generalized cyclotomic polynomials and generalized Dickson polynomials of the first kind of order , over finite field . 相似文献
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Edoardo Ballico 《Quaestiones Mathematicae》2016,39(1):1-8
Some evaluation methods of multivariate polynomials over finite fields are described and their multiplicative complexity is discussed. 相似文献
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