An L Inequality for ‘self-reciprocal’ Polynomials. Ii
نویسنده
چکیده
The main result of this paper is a sharp integral mean inequality for the derivative of a ‘self-reciprocal’ polynomial.
منابع مشابه
On Zeros of Reciprocal Polynomials of Odd Degree
The first author [1] proved that all zeros of the reciprocal polynomial Pm(z) = m ∑ k=0 Akz k (z ∈ C), of degree m ≥ 2 with real coefficients Ak ∈ R (i.e. Am 6= 0 and Ak = Am−k for all k = 0, . . . , [ m 2 ] ) are on the unit circle, provided that |Am| ≥ m ∑ k=0 |Ak −Am| = m−1 ∑ k=1 |Ak −Am|. Moreover, the zeros of Pm are near to the m + 1st roots of unity (except the root 1). A. Schinzel [3] g...
متن کاملSome Properties of Generalized Self-reciprocal Polynomials over Finite Fields
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to aself reciprocal polynomials defined in [4]. We consider the properties for the divisibility of a-reciprocal polynomials, estimate the number of all nontrivial a-self reciprocal irreducible monic polynomials and characterize the parity of the number of irreducible f...
متن کاملBernstein's polynomials for convex functions and related results
In this paper we establish several polynomials similar to Bernstein's polynomials and several refinements of Hermite-Hadamard inequality for convex functions.
متن کاملSelf-reciprocal Polynomials Over Finite Fields
The reciprocal f ∗(x) of a polynomial f(x) of degree n is defined by f ∗(x) = xf(1/x). A polynomial is called self-reciprocal if it coincides with its reciprocal. The aim of this paper is threefold: first we want to call attention to the fact that the product of all self-reciprocal irreducible monic (srim) polynomials of a fixed degree has structural properties which are very similar to those o...
متن کاملOn the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials
Let q be a power of an odd prime and let k, n ∈ N such that 1 < k ≤ n. We investigate the existence of self-reciprocal irreducible monic polynomials over Fq, of degree 2n and their k-th coefficient prescribed.
متن کامل