Related papers: Zeros and coefficients
In this paper, asymptotic behavior of convolution of distributions belonging to two subclasses of distributions with exponential tails are considered, respectively. The precise second-order tail asymptotics of the convolutions are derived…
We study distribution of zeros of a complex polynomial whose coefficients has been modified. We give a new proof of the theorem of Rubinstein, and with similar method we prove a new theorem that is not generalization of the previous…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…
The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.
The main result of the paper determines all real meromorphic functions of finite order in the plane for which the first derivative has finitely many zeros, while the function itself and one of its higher derivatives have finitely many…
Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.
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 paper solves the problems of determining the asymptotics of the number of primes and the sums of functions of primes in a subset of the natural series that satisfies the conditions that the asymptotic density of the number of primes in…
In this note, we study asymptotic zero distribution of multivariable full system of random polynomials with independent Bernoulli coefficients. We prove that with overwhelming probability their simultaneous zeros sets are discrete and the…
We propose the construction of entire functions with a given random collection of zeros. There are considered two particular cases. In the first one we are dealing with simple zeros. And the second corresponds to random zeros with random…
We study the distribution of zeros of general solutions of the Airy and Bessel equations in the complex plane. Our results characterize the patterns followed by the zeros for any solution, in such a way that if one zero is known it is…
Whenever all differences between zeros of two holomorphic almost periodic functions in a strip form a discrete set, then both functions are infinite products of periodic functions with commensurable periods. In particular, the result is…
Asymptotic integration theory gives a collection of results which provide a thorough description of the asymptotic growth and zero distribution of solutions of (*) $f''+P(z)f=~0$, where $P(z)$ is a polynomial. These results have been used…
We study the asymptotic behaviour of convolution-type functionals defined on general periodic domains by proving an extension theorem
Numerical study of the distribution of the Riemann zeros differences following the work [1] shows the significance of the function for which the prime sum expression is proposed. Computational results related to this definition explored…
Normalized exponential sums are entire functions of the form $$ f(z)=1+H_1e^{w_1z}+\cdots+H_ne^{w_nz}, $$ where $H_1,\ldots, H_n\in\C$ and $0<w_1<\ldots<w_n$. It is known that the zeros of such functions are in finitely many vertical strips…
We consider a sum of the derivatives of Dirichlet $L$-functions over the zeros of Dirichlet $L$-functions. We give an asymptotic formula for the sum.
The derivative of a polynomial with all zeros on the unit circle has the zeros of its derivative on or inside the unit circle. It has been observed that in many cases the zeros of the derivative have a bimodal distribution: there are two…
In this paper we prove a universal inequality describing the asymptotic behavior of support points for planar continuous curves. As corollaries we get an analogous result for tangent points of differentiable planar curves and some…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…