Related papers: Zeros and coefficients
We examine the counting function for rational points on conics, and show how the point where the asymptotic behaviour begins depends on the size of the smallest zero.
We consider the zeros distributions on the derivatives of difference polynomials of meromorphic functions, and present some results which can be seen as the discrete analogues of Hayman conjecture \cite{hayman1}, also partly answer the…
The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…
The main aim of this paper is twofold. First we generalize, in a novel way, most of the known non-vanishing results for the derivatives of the Riemann zeta function by establishing the existence of an infinite sequence of regions in the…
We present a remarkable connection between the asymptotic behavior of the Riemann zeros and one-loop effective action in Euclidean scalar field theory. We show that in a two-dimensional space, the asymptotic behavior of the Fourier…
Four propositions are considered concerning the relationship between the zeros of two combinations of the Riemann zeta function and the function itself. The first is the Riemann hypothesis, while the second relates to the zeros of a…
We find the asymptotics of the counting function of zeroes of random entire functions represented by Rademacher Taylor series. We also give the asymptotics of the weighted counting function, which takes into account the arguments of zeroes.…
We derive the large $n$ asymptotics of zeros of sections of a generic exponential sum. We divide all the zeros of the $n$-th section of the exponential sum into ``genuine zeros'', which approach, as $n\to\infty$, the zeros of the…
The real and complex zeros of the parabolic cylinder function $U(a,z)$ are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and these are valid for $a$ positive or negative and large in…
Following Wiener, we consider the zeroes of Gaussian analytic functions in a strip in the complex plane, with translation-invariant distribution. We show that the variance of the number of zeroes in a long horizontal rectangle $[0,T]\times…
We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the…
A result is proved concerning meromorphic functions of finite order in the plane such that all but finitely many zeros of the second derivative are zeros of the first derivative.
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
In this work, it is introduced a new function based on the non-trivial zeros of the Riemann-zeta function. Such function shows an interesting behavior: when the argument of the function grows, it changes from a pseudo-random behavior to a…
We derive two distinct asymptotic expansions for the zeros $j_{\nu,k}^{(n)}$ of the $n$-th derivative of Bessel function $J_\nu^{(n)}(x)$. The first is a McMahon-type expansion for the case when $k \to \infty$ with fixed $\nu$, for which we…
Some results are proved concerning asymptotic and deficient values in connection with the second order linear differential equation $y'' + Ay = 0$, in which the coefficient $A$ is entire.
The existence of non trivial zeros off the critical line for a function obtained by analytic continuation of a particular Dirichlet series is studied. Contrary to what has been presumed for a long time, we prove that such zeros cannot…
By random complex zeroes we mean the zero set of a random entire function whose Taylor coefficients are independent complex-valued Gaussian variables, and the variance of the k-th coefficient is 1/k!. This zero set is distribution invariant…
A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis…
In this paper, we establish a simple criterion for two $L$-functions $L_1$ and $L_2$ satisfying a functional equation (and some natural assumptions) to have infinitely many distinct zeros. Some related questions have already been answered…