Related papers: Zeros of Meromorphic function
W. Luo has investigated the distribution of zeros of the derivative of the Selberg zeta function associated to compact hyperbolic Riemann surfaces. In essence, the main results in Luo's article involve the following three points: Finiteness…
The zeros of semi-orthogonal functions with respect to a probability measure mu supported on the unit circle can be applied to obtain Szego quadrature formulas. The discrete measures generated by these formulas weakly converge to the…
We survey results and conjectures concerning the zero distribution of chromatic and flow polynomials of graphs, and characteristic polynomials of matroids.
We investigate questions of an arithmetic nature related to the Abel-Jacobi map. We give a criterion for the zero locus of a normal function to be defined over a number field, and we give some comparison theorems with the Abel-Jacobi map…
We extend the circle theorem on the zeros of the partition function to a continuum system. We also calculate the exact zeros of the partition function for a finite system where the probability distribution for the order parameter is given…
We extend the matrix-resolvent method for computing logarithmic derivatives of tau-functions to the Ablowitz--Ladik hierarchy. In particular, we derive a formula for the generating series of the logarithmic derivatives of an arbitrary…
A number of results are proved concerning non-real zeros of derivatives of real meromorphic functions. In particular, the paper supersedes the previous arXiv submission "Non-real zeros of linear differential polynomials in real meromorphic…
The zeros of the size-$n$ partition functions for a statistical mechanical model can be used to help understand the critical behaviour of the model as $n\to\infty$. Here we use weighted Dyck paths as a simple model of two-dimensional…
We show that for a real transcendental meromorphic function f, the differential polynomial f'+f^m with m > 4 has infinitely many non-real zeros. Similar results are obtained for differential polynomials f'f^m-1. We specially investigate the…
A connection between the zeta functions of zeros and poles of a meromorphic function has been established, and using it, a criterion for the absence of zeros has been derived. Sufficient conditions for the existence of zeros of sums of…
In this article we consider functions $f$ meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions. This condition simplifies and generalizes known conditions. We…
This paper investigates the expected number of complex roots of nonlinear equations. Those equations are assumed to be analytic, and to belong to certain inner product spaces. Those spaces are then endowed with the Gaussian probability…
Singular sectors $\mathcal{Z}_{\mathrm{sing}}$ (loci of zeros) for real-valued non-positively defined partition functions $\mathcal{Z}$ of $n$ variables are studied. It is shown that $\mathcal{Z}_{\mathrm{sing}}$ have a stratified structure…
We study the distribution of the zeros of functions of the form $f(s)=h(s) \pm h(2a-s)$, where $h(s)$ is a meromorphic function, real on the real line, $a$ a real number. One of our results establishes sufficient conditions under which all…
In this note we extend the Dirac method to partial differential equations involving higher order roots of differential operators.
Theta functions play a major role in many current researches and are powerful tools for studying integrable systems. The purpose of this paper is to provide a short and quick exposition of some aspects of meromorphic theta functions for…
We demonstrate that Wan's alternate description of Dwork's unit root L-function in the rank one case may be modified to give a proof of meromorphy that is classical, eliminating the need to study sequences of uniform meromorphic functions.
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
We show that the dilogarithm has at most one zero on each branch, that each zero is close to a root of unity, and that they may be found to any precision with Newton's method. This work is motivated by applications to the asymptotics of…
We interpret a formula for meromorphic functions on foliations by Riemann surfaces as an analogue to the product formula of valuations in algebraic number theory.