We study statistical properties of zeros of random polynomials and random analytic functions associated with the pseudoeuclidean group of symmetries SU(1, 1), by utilizing both analytical and numerical techniques. We first show that zeros of the SU(1, 1) random polynomial of degree N are concentrated in a narrow annulus of the order of N around the unit circle on the complex plane, and we find ...

In a classical work of the 1950’s, Lee and Yang proved that for fixed nonnegative temperature, the zeros of the partition functions of a ferromagnetic Ising model always lie on the unit circle in the complex magnetic field. Zeros of the partition function in the complex temperature were then considered by Fisher, when the magnetic field is set to zero. Limiting distributions of Lee-Yang and of ...

In a classical work of the 1950’s, Lee and Yang proved that for fixed nonnegative temperature, the zeros of the partition functions of a ferromagnetic Ising model always lie on the unit circle in the complex magnetic field. Zeros of the partition function in the complex temperature were then considered by Fisher, when the magnetic field is set to zero. Limiting distributions of Lee-Yang and of ...

Let G(z) be a real entire function of order less than 2 with only real zeros. Then we classify certain distributions functions F such that the convolution (G ∗ dF )(z) = ∫∞ −∞G(z − is) dF (s) has only real zeros.

We compute zeros off the critical line of a Dirichlet series considered by H. Davenport and H. Heilbronn. This computation is accomplished by deforming a Dirichlet series with a set of known zeros into the DavenportHeilbronn series.

Abstract: The probability that a random polynomial of degree n with i.i.d exponentially distributed coefficients has all real zeros is P(All zeros are real) = E ∏ 1≤j<k≤n |Uj − Uk| = ( n−1 ∏

In this study, we apply Walker et al.’s (1994) centering account of Japanese zero elements to Korean correspondents, and we evaluate whether their analysis provides the correct interpretation of zeros. We investigate whether Korean pronouns and zeros are treated as the same sort of entities during semantic interpretation. In a psycholinguistics experiment, we test Walker et al. (1994) by compar...

There is an intimate connection between the distribution of the nontrivial zeros of the Riemann zeta function ζ(s) and the distribution of prime numbers. Critical to many prime number problems is the horizontal distribution of zeros; here the Riemann Hypothesis (RH) asserts that the zeros all have real part 1 2 . There is also much interest in studying the distribution of the imaginary parts of...

In a classical work of the 1950’s, Lee and Yang proved that for fixed nonnegative temperature, the zeros of the partition functions of a ferromagnetic Ising model always lie on the unit circle in the complex magnetic field. Zeros of the partition function in the complex temperature were then considered by Fisher, when the magnetic field is set to zero. Limiting distributions of Lee-Yang and of ...

with the initial values G0(x) = a and G1(x) = x + b. The polynomials Gn−1(1, 0;x) and Gn(2, 0;x)(n ≥ 1) are just the usual Fibonacci polynomials Fn(x) and the Lucas polynomials Ln(x), respectively. Our concern in this paper is to study some of the properties of the zeros of the Fibonacci-type polynomials Gn(a, b;x). The zeros of Fn(x) and Ln(x) have been given explicitly by V. E. Hoggatt, Jr. a...