Means of algebraic numbers in the unit disk
نویسنده
چکیده
Schur studied limits of the arithmetic means sn of zeros for polynomials of degree n with integer coefficients and simple zeros in the closed unit disk. If the leading coefficients are bounded, Schur proved that lim supn→∞ |sn| ≤ 1− √ e/2. We show that sn → 0, and estimate the rate of convergence by generalizing the Erdős-Turán theorem on the distribution of zeros. To cite this article: I. E. Pritsker, C. R. Acad. Sci. Paris, Ser. I 336 (2003).
منابع مشابه
Distribution of Algebraic Numbers
Schur studied limits of the arithmetic means An of zeros for polynomials of degree n with integer coefficients and simple zeros in the closed unit disk. If the leading coefficients are bounded, Schur proved that lim supn→∞ |An| ≤ 1 − √ e/2. We show that An → 0, and estimate the rate of convergence by generalizing the Erdős-Turán theorem on the distribution of zeros. As an application, we show t...
متن کاملA Class of Quadrinomial Garsia Numbers
Real algebraic integers larger than 1 whose minimal polynomials are certain quadrinomials of degree at least 5 with constant term ±2 and all roots outside the closed unit disk are determined and some of their properties are mentioned.
متن کاملON SOME STRUCTURES OF FUZZY NUMBERS
The operations in the set of fuzzy numbers are usually obtained bythe Zadeh extension principle. But these definitions can have some disadvantagesfor the applications both by an algebraic point of view and by practicalaspects. In fact the Zadeh multiplication is not distributive with respect tothe addition, the shape of fuzzy numbers is not preserved by multiplication,the indeterminateness of t...
متن کاملNew results on p-Carleson measures and some related measures in the unit disk
We provide some new sharp embeddings for p-Carleson measures and some related measures in the unit disk of the complex plane.
متن کاملRepresentation of $H$-closed monoreflections in archimedean $ell$-groups with weak unit
The category of the title is called $mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $mathcal{A}$, $Hmathcal{A}$ consists of all homomorphic images of $mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(mathcal{R}, r)$ (meaning $Hmathcal{R} = mathcal{R}$), about which we show ({em inter alia}): $A in mathcal{A}$ if and only if...
متن کامل