the aim of this note is to characterize the finite groups in which all non-linear irreducible characters have distinct zero entries number.

In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, we obtain the zeros of eigenfunctions.

The zeros of generalized Krawtchouk polynomials are studied. Some interlacing theorems for the zeros are given. A new infinite family of integral zeros is given, and it is conjectured that these comprise most of the non-trivial zeros. The integral zeros for two families of q-Krawtchouk polynomials are classified.

We obtain exact analytical expressions for correlations between real zeros of the Kac random polynomial. We show that the zeros in the interval (−1, 1) are asymptotically independent of the zeros outside of this interval, and that the straightened zeros have the same limit translation invariant correlations. Then we calculate the correlations between the straightened zeros of the SO(2) random p...

the aim of this paper is to classify the finite simple groups with the number of zeros at most seven greater than the number of nonlinear irreducible characters in the character tables. we find that they are exactly a$_{5}$, l$_{2}(7)$ and a$_{6}$.

The notions separability and normality are related to this characterisation. In the case of skew fields polynomials often have infinitely many zeros, so a different way of counting zeros as distinct is needed. The well-known theorem of Gordon and Motzkin [Z] states that a polynomial of degree n has zeros in at most n conjugacy classes. This suggests one should count zeros of a polynomial by the...

Abstract. The complex zeros of the Riemannn zeta-function are identical to the zeros of the Riemann xi-function, ξ(s). Thus, if the Riemann Hypothesis is true for the zetafunction, it is true for ξ(s). Since ξ(s) is entire, the zeros of ξ(s), its derivative, would then also satisfy a Riemann Hypothesis. We investigate the pair correlation function of the zeros of ξ(s) under the assumption that ...

In the noncommutative case also a version of (1) can be proved; see for instance [S, Proposition A.33. In that case, in general, such an N is not finitely generated over K. What (2) means for the noncommutative case depends on how one defines the phrase “constructing by repeatedly adding zeros of p until p has a complete set of zeros.” The adding of zeros may be done by forming field coproducts...

Polynomials with perturbed coefficients, which can be regarded as interval polynomials, are very common in the area of scientific computing due to floating point operations in a computer environment. In this paper, the zeros of interval polynomials are investigated. We show that, for a degree n interval polynomial, the number of interval zeros is at most n and the number of complex block zeros ...