where l > 0 and {dk0, dk1} is a so-called symmetrically coherent pair, with dk0 or dk1 the classical Gegenbauer measure (x−1) dx, a > −1. If dk1 is the Gegenbauer measure, then Sn has n different, real zeros. If dk0 is the Gegenbauer measure, then Sn has at least n−2 different, real zeros. Under certain conditions Sn has complex zeros. Also the location of the zeros of Sn with respect to Gegenb...

Unstable zeros limit the achievable control performance. When a continuous-time system is discretized using the zero-order hold, there is no simple relation which shows how the zeros of the continuous-time system are transformed by sampling. This paper analyzes the asymptotic behavior of the limiting zeros for multivariable systems and derives a new condition for the zeros to be stable for suff...

We obtain counterparts of the Lindelöf theorem on types entire functions whose growth is determined by Boutroux proximate order. The results are formulated in terms upper density zeros a function and balance its zeros.

Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated. Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds fo...

Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated. Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds fo...

in this paper, we investigate infinite product representation of the solution of a sturm-liouville equation with an indefinite weight function which has two zeros and/or singularitiesin a finite interval. first, by using of the asymptotic estimates provided in [w. eberhard, g.freiling, k. wilcken-stoeber, indefinite eigenvalue problems with several singular pointsand turning points, math. nachr...

Given an analytic function f and a Jordan curve γ that does not pass through any zero of f , we consider the problem of computing all the zeros of f that lie inside γ, together with their respective multiplicities. Our principal means of obtaining information about the location of these zeros is a certain symmetric bilinear form that can be evaluated via numerical integration along γ. If f has ...

This subject started with H. L. Montgomery’s famous paper [12], where he introduced a method to study the vertical distribution of the zeros of the Riemann zeta-function. Assuming the Riemann Hypothesis, he calculated the pair correlation of the zeros and from it deduced an estimate for the size of small gaps between the zeros and for the percentage of simple zeros. This paper opened a whole ne...

The Yang-Lee zeros of the Q-state Potts model are investigated in 1, 2 and 3 dimensions. Analytical results derived from the transfer matrix for the one-dimensional model reveal a systematic behavior of the locus of zeros as a function of Q. For 1 < Q < 2 the zeros in the complex x = exp(βHq) plane lie inside the unit circle, while for Q > 2 they lie outside the unit circle for finite temperatu...