arXiv subjects

Tamas Erdelyi

Publications and source records attributed to Tamas Erdelyi.

8 recordsLinked to original sources

arXiv2022

Asymptotic Directions for the Zero Sets of the Components of an Electrical Field from a Finite Number of Point Charges on the Plane Part II

We study the structure of the zero set of a nontrivial finite point charge electrical field $F = (X,Y)$ in the plane $\mathbb R^2$. We establish equations satisfied by the possible directions for the zero sets \{X = 0\} and $\{Y = 0\}$ separately, and we show that there are only finitely many possible asymptotic directions for both of these zero sets. We suspect that the set of asymptotic directions for \{X = 0\} and the set of asymptotic directions for $\{Y = 0\}$ are (essentially) distinct.

math.CA↗

arXiv2016

The number of unimodular zeros of self-reciprocal polynomials with coefficients in a finite set

We study the number of real zeros of trigonometric polynomials in a period and the number of zeros of self-reciprocal algebraic polynomials on the unit circle under the assumption that their coefficients are in a fixed finite set of real numbers.

math.CA↗

arXiv2016

Inequalities for exponential sums

Inequalities for exponential sums are studied. Our results improve an old result of G. Halasz and a recent result of G. Kos. We prove several other essentially sharp related results in this paper.

math.CA↗

arXiv2014

A note on Barker polynomials

We give a new proof of the fact that Barker polynomials of even degree greater than 12, and hence Barker sequences of odd length greater than 13 do not exist. This is intimately tied to irreducibility questions and proved as a consequence of a new result.

math.NT↗

arXiv2014

M. Riesz-Schur-type inequalities for entire functions of exponential type

We prove a general M. Riesz-Schur-type inequality for entire functions of exponential type.

math.CV↗

arXiv2014

Inequalities for Lorentz polynomials

We prove a few interesting inequalities for Lorentz polynomials including Nikolskii-type inequalities. A highlight of the paper is a sharp Markov-type inequality for polynomials of degree at most n with real coefficients and with derivative not vanishing in the open unit disk. The result may be compared with Erdos's classical Markov-type inequality (1940) for polynomials of degree at most n having only real zeros outside the interval (-1,1).

math.CA↗

arXiv2014

Coppersmith-Rivlin type inequalities and the order of vanishing of polynomials at 1

We examine the maximal number of zeros a polynomial of degree at most n with constrained coefficients may have at 1. Our results are essentially sharp and extend earlier results of this variety. An interesting connection to certain extensions of the Coppersmith-Rivlin inequality is explored.

math.NT↗

arXiv2014

The Mahler measure of the Rudin-Shapiro polynomials

Littlewood polynomials are polynomials with each of their coefficients in {-1,1}. A sequence of Littlewood polynomials that satisfies a remarkable flatness property on the unit circle of the complex plane is given by the Rudin-Shapiro polynomials. It is shown in this paper that the Mahler measure and the maximum modulus of the Rudin-Shapiro polynomials on the unit circle of the complex plane have the same size. It is also shown that the Mahler measure and the maximum norm of the Rudin-Shapiro polynomials have the same size even on not too small subarcs of the unit circle of the complex plane. Not even nontrivial lower bounds for the Mahler measure of the Rudin Shapiro polynomials have been known before.

math.CV↗