In 1972 Montgomery [20, 21] introduced a new method for studying the zeros of the Riemann zeta-function. One of his main accomplishments was to determine partially the pair correlation of zeros, and to apply his results to obtain new information on multiplicity of zeros and gaps between zeros. Perhaps more importantly, he conjectured on number-theoretic grounds an asymptotic formula for the pai...

It is well known that multirate input and hold, such as a generalized sample hold function (GSHF), can be used to shift the sampling zeros of a discrete-time model for a continuous-time system. This paper deals with the stability of sampling zeros, as the sampling period tends to zero, of discrete-time models that are composed of a GSHF, a continuous-time multivariable plant and a sampler in ca...

The Riemann hypothesis is identified with zeros of N = 4 supersymmetric gauge theory four-point amplitude. The zeros of the ζ(s) function are identified with th complex dimension of the spacetime, or the dimension of the toroidal compactification. A sequence of dimensions are identified in order to map the zeros of the amplitude to the Riemann hypothesis.

with s = 12 + it , and shows that ξ(t) is an even entire function of t whose zeros have imaginary part between −i/2 and i/2. He further states, sketching the proof, that in the range between 0 and T the function ξ(t) has about (T/2π) log(T/2π)− T/2π zeros. Riemann then continues: “Mann finden nun in der That etwa so wiel reelle Nullstellen innerhalb dieser Grenzen, und es ist sehr wahrscheinlic...

In this article, we show that the Riemann hypothesis for an $L$-function $F$ belonging to Selberg class implies all derivatives of can have at most finitely many zeros on left critical line with imaginary part greater than a certain constant. This was shown zeta function by Levinson and Montgomery in 1974.

A classical result due to Cohn states that a self-inversive polynomial has all its zeros on the unit circle if and only if all the zeros of its derivative lie in the closed unit disk. A more flexible necessary and sufficient condition than that of Cohn’s was given by Chen. However those results do not give any information on the simplicity of zeros of a self-inversive polynomial. This paper mod...

The geometry of polynomials explores geometrical relationships between the zeros and the coefficients of a polynomial. A classical problem in this theory is to locate the zeros of a given polynomial by determining disks in the complex plane in which all its zeros are situated. In this paper, we infer bounds for general polynomials and apply classical and new results to graph polynomials namely ...