Related papers: The random Weierstrass zeta function I. Existence,…

In this paper we consider a discrete-time dynamical system on the real line by random iteration of two functions. These functions are assumed to satisfy appropriate monotonicity conditions; optionally, a symmetry condition may be imposed.…

This theorem is based on holomorphy of studied functions and the fact that near a singularity point the real part of some rational function can take an arbitrary preassigned value.

We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…

We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…

Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(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.

We prove an equivalent of the Riemann hypothesis in terms of the functional equation (in its asymmetrical form) and the $a$-points of the zeta-function, i.e., the roots of the equation $\zeta(s)=a$, where $a$ is an arbitrary fixed complex…

Stationary points or derivative zero crossings of a regression function correspond to points where a trend reverses, making their estimation scientifically important. Existing approaches to uncertainty quantification for stationary points…

In the theory of elliptic functions and elliptic curves, the Weierstrass $zeta$ function (which is essentially an antiderivative of the Weierstrass $\wp$ function) plays a prominent role. Although it is not an elliptic function, Eisenstein…

It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the whole complex plane. But, in the case of general ($C^{\infty}$) smooth functions, the meromorphic…

We investigate the horizontal distribution of zeros of the derivative of the Riemann zeta function and compare this to the radial distribution of zeros of the derivative of the characteristic polynomial of a random unitary matrix. Both…

The Riemann -Rock theorem plays a central role in the theory of Riemann surfaces with applications to several branches in Mathematics and Physics. Suppose $X$ ia a compact Riemann surface of genus $g$ and $P \in X$. By the Riemann-Roch…

Results of extensive computations of moments of the Riemann zeta function on the critical line are presented. Calculated values are compared with predictions motivated by random matrix theory. The results can help in deciding between those…

In this short manuscript, we will put some light on the different outcomes when two non-constant meromorphic functions share a value with prescribed weight two.

We present methods that provide all zeroes and extrema of a function that do not require differentiation. Using point process theory, we are able to describe the locations of zeroes or maxima, their number, as well as their distribution…

We study the number of the poles of the meromorphic continuation of the dynamical zeta functions $\eta_N$ and $\eta_D$ for several strictly convex disjoint obstacles satisfying non-eclipse condition. We obtain a strip $\{z \in \mathbb C:\:…

We show that it is possible to generate a random walk with an electrostatic field by means of several parallel infinite charged planes in which the surface charge distribution could be either $\pm\sigma$. We formulate the problem of this…

We give explicit definitions of the Weierstrass elliptic functions $\wp$ and $\zeta$ in terms of pfaffian functions, with complexity independent of the lattice involved. We also give such a definition for a modification of the Weierstrass…

We discuss about the conjectural cohomological theory of dynamical zeta functions in the case of general Anosov flows. Our aim is to provide a functional-analytic framework that enables us to justify the basic part of the theory rigorously.…

The partition function for the random walk of an electrostatic field produced by several static parallel infinite charged planes in which the charge distribution could be either $\pm\sigma$ is obtained. We find the electrostatic energy of…

We investigate the first-order system `$s\,' = c^3, \, c\,' = - s^3; \, s(0) = 0, \, c(0) = 1$'. Its solutions have the property that $s \, c$, $s^2$ and $c^2$ extend to simply-poled elliptic functions, which we explicitly identify in terms…