On the Existence of Roots of Some p-adic Exponential-Polynomials

In this paper, we use the Newton polygon of certain p-adic exponential polynomials in order to nd sufficient conditions for the existence of zeros.

The Zeros of the Bergman Kernel for Some Reinhardt Domains

We consider the Reinhardt domainDn={(ζ,z)∈C×Cn:|ζ|2<(1-|z1|2)⋯(1-|zn|2)}.We express the explicit closed form of the Bergman kernel forDnusing the exponential generating function for the Stirling number of the second kind. As an application, we show that the Bergman kernelKnforDnhas zeros if and only ifn≥3. The study of the zeros ofKnis reduced to some real polynomial with coefficients which are related to Bernoulli numbers. This result is a complete characterization of the existence of zeros of the Bergman kernel forDnfor all positive integersn.

Front instability in a condensed phase combustion model

We consider a condensed phase (or solid) combustion model and its linearization around the travelling front solution. We construct an Evans function to characterize the eigenvalues of the linearized problem. We estimate this functional in the high activation energy limit. We deduce the existence of zeros with nonnegative real part for high activation energy, which proves the linear instability of the travelling front solution.

On the zeros of Epstein zeta functions

We investigate the zeros of Epstein zeta functions associated with a positive definite quadratic form with rational coefficients. Davenport and Heilbronn, and also Voronin, proved the existence of zeros of Epstein zeta functions off the critical line when the class number of the quadratic form is bigger than 1. These authors give lower bounds for the number of zeros in strips that are of the same order as the more easily proved upper bounds. In this paper, we improve their results by providing asymptotic formulas for the number of zeros.

INFINITE DIMENSIONAL KRAWCZYK OPERATOR FOR FINDING PERIODIC ORBITS OF DISCRETE DYNAMICAL SYSTEMS

In this work, we introduce the Krawczyk operator for infinite dimensional maps. We prove two properties of this operator related to the existence of zeros of the map. We also show how the Krawczyk operator can be used to prove the existence of periodic orbits of infinite dimensional discrete dynamical systems and for finding all periodic orbits with a given period enclosed in a specified region. As an example, we consider the Kot–Schaffer growth-dispersal model, for which we find all fixed points and period-2 orbits enclosed in the region containing the attractor observed numerically.

Zeros of differences of meromorphic functions

Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(z) = Δf(z) = f(z + 1) − f(z). A number of results are proved concerning the existence of zeros of g(z) or g(z)/f(z), in terms of the growth and the poles of f. The results may be viewed as discrete analogues of existing theorems on the zeros of f' and f'/f.