BOUNDS FOR ZEROS OF THE CHARLIER POLYNOMIALS ∗ (2008)
Abstract. We use the method of positive quadratic forms and discrete analogues of the Laguerre inequality recently obtained by the author, to give bounds on the zeros of the Charlier polynomials,...
School of Mathematical Sciences, (2007)
We derive new estimates for the range where the distance distribution of a code is upperbounded by the corresponding normalized binomial distribution. The estimates depend on the code's dual...
Linear Programming Bounds for Codes of Small Size (2007)
Combining linear programming approach with the Plotkin-Johnson argument for constant weight codes, we derive upper bounds on the size of codes of length n and minimum distance d = (n 0 j)=2, 0 ! j !...
On Distribution of Exponential Sums in Fields of Characteristic Two (2007)
Distribution of the values of exponential sums in finite fields of characteristic two is considered. We derive upper bounds on the individual components of this distribution. 1 Introduction Let F = F...
On Erd\'{e}lyi-Magnus-Nevai conjecture for Jacobi polynomials (2006)
T. Erd\'{e}lyi, A.P. Magnus and P. Nevai conjectured that for $\alpha, \beta \ge - {1/2} ,$ the orthonormal Jacobi polynomials ${\bf P}_k^{(\alpha, \beta)} (x)$ satisfy the inequality...
An upper bound on Jacobi polynomials (2006)
Let ${\bf P}_k^{(\alpha, \beta)} (x)$ be an orthonormal Jacobi polynomial of degree $k.$ We will establish the following inequality \begin{equation*} \max_{x \in [\delta_{-1},\delta_1]}\sqrt{(x-...
Upper Bounds on the Automorphism Group of a Graph (2006)
Krasikov, Ilia, Lev, Arie, Thatte, Bhalchandra D.
We give upper bounds on the order of the automorphism group of a simple graph
Turán Inequalities and Zeros of Orthogonal Polynomials (2005)
We use Turán type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal...
New bounds on the Hermite polynomials (2004)
We shall establish two-side explicit inequalities, which are asymptotically sharp up to a constant factor, on the maximum value of $|H_k(x)| e^{-x^2/2},$ on the real axis, where $H_k$ are the Hermite...
Turan inequalities and zeros of orthogonal polynomials (2004)
We use Turan type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal...
On extreme zeros of classical orthogonal polynomials (2003)
Let $x_1$ and $x_k$ be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree $k.$ We shall establish sharp inequalities of the form $x_1 B,$ which are uniform in all the...
On zeros of polynomials and allied functions satisfying second order differential equations (2002)
We shall give bounds on the spacing of zeros of certain functions belonging to the Laguerre-Polya class and satisfying a second order differential equation. As a corollary we establish new sharp...
Bounds for the 3x+1 Problem using Difference Inequalities (2002)
Krasikov, Ilia, Lagarias, Jeffrey C.
We study difference inequality systems for the 3x+1 problem introduced by the first author in 1989. These systemes can be used to give lower bounds for the number of integers below x that contain 1...
Multiplicity of zeros and discrete orthogonal polynomials (2002)
We consider a problem of bounding the maximal possible multiplicity of a zero at of some expansions $\sum a_i F_i(x)$, at a certain point $c,$ depending on the chosen family $\{F_i \}$. The most...
Dicrete Analogues of the Laguerre Inequality (2002)
It is shown that $\sum_{j=-m}^m (-1)^j \frac{f(x-j)(f(x+j)}{(m-j)! (m+j)!} \ge 0,$ $m=0,1,...,$ where $f(x)$ is either a real polynomial with only real zeros or an allied entire function of a special...
Bounds on Spectra of Codes with Known Dual Distance (1998)
. We estimate the interval where the distance distribution of a code of length n and of given dual distance is upperbounded by the binomial distribution. The binomial upper bound is shown to be sharp...
Linear Programming Bounds for Doubly-Even Self-Dual Codes (1997)
We give a new proof of the Mallows-Sloane bound on the minimum distance of doubly-even self-dual codes. The proof avoids using the Gleason theorem and invariant theory. It is based on a special...
On Integral Zeros of Krawtchouk Polynomials (1996)
We derive new conditions for nonexistence of integral zeros of binary Krawtchouk polynomials. Upper bounds for the number of integral roots of Krawtchouk polynomials are presented. Keywords:...
On Accuracy of Binomial Approximation to the Distance Distribution of Codes (1995)
The binomial distribution is a well known approximation to the distance spectra of many classes of codes. We derive a lower estimate for the deviation from the binomial approximation. Keywords:...
On Spectra of BCH Codes (1995)
We derive an estimate for the error term in the binomial approximation of spectra of BCH codes. This estimate asymptotically improves on the earlier bounds by Sidelnikov, Kasami-Fujiwara-Lin and...
An Improved Upper Bound on the Minimum Distance of Doubly-Even Self-Dual Codes
We derive a new upper bound on the minimum distance d of doubly-even self-dual codes of length n. Asymptotically, for n growing, it gives lim n!1 sup d=n (5 \Gamma 5 3=4 )=10 ! 0:165630, thus...