20 citations · 21 across the 10 of their papers we have counts for
14 papers
On the oscillations of the modulus of Rudin-Shapiro polynomials around the middle of their ranges
Tamás Erdélyi
Let either or , where and are the usual Rudin-Shapiro polynomials of degree with . The graphs of the…
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
Tamas Erdelyi, Joseph Rosenblatt, Rebecca Rosenblatt
We study the structure of the zero set of a nontrivial finite point charge electrical field in the plane . We establish equations satisfied by the possible…
The asymptotic distance between an ultraflat unimodular polynomial and its conjugate reciprocal
Tamás Erdélyi
Let A sequence of polynomials $P_n \in {\mat…
The sharp Remez-type inequality for even trigonometric polynomials on the period
Tamás Erdélyi
We prove that for every even trigonometric polynomia…
The asymptotic value of the Mahler measure of the Rudin-Shapiro polynomials
Tamás Erdélyi
In signal processing the Rudin-Shapiro polynomials have good autocorrelation properties and their values on the unit circle are small. Binary sequences with low autocorrelation coe…
Improved lower bounds for the Mahler measure of the Fekete polynomials
Tamás Erdélyi
We show that there is an absolute constant such that the Mahler measure of the Fekete polynomials of the form $$f_p(z) := \sum_{k=1}^{p-1}{\left( \frac kp \right)z^…
On the oscillation of the modulus of the Rudin-Shapiro polynomials on the unit circle
Tamás Erdélyi
In signal processing the Rudin-Shapiro polynomials have good autocorrelation properties and their values on the unit circle are small. Binary sequences with low autocorrelation coe…
Improved lower bound for the number of unimodular zeros of self-reciprocal polynomials with coefficients in a finite set
Tamás Erdélyi
Let be non-negative integers. In a private communication Brian Conrey asked how fast the number of real zeros of the trigonometric polynomials $T_N(θ) =…
The number of unimodular zeros of self-reciprocal polynomials with coefficients in a finite set
Tamas Erdelyi
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…
Inequalities for Lorentz polynomials
Tamas Erdelyi
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…
Coppersmith-Rivlin type inequalities and the order of vanishing of polynomials at 1
Tamas Erdelyi
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…
A note on Barker polynomials
Peter Borwein, Tamas Erdelyi
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 ti…
Chebyshev constants for the unit circle
Gergely Ambrus, Keith M. Ball, T. Erdélyi
It is proven that for any system of n points z_1, ..., z_n on the (complex) unit circle, there exists another point z of norm 1, such that Equality…
The size of exponential sums on intervals of the real line
Tamás Erdélyi, Kaveh Khodjasteh, Lorenza Viola
We prove that there is a constant depending only on and such that for every of…