Related papers: Zeros of new Bergman kernels

We study the value-distribution of Dirichlet polynomials on the critical line $\Re(s)=\tfrac{1}{2}$. As a consequence, we prove a corollary on small consecutive gaps between zeros of the Riemann zeta function. We also examine the…

We study the reproducing kernel for weighted polynomial Bergman spaces and consider applications to the Berezin transform. Some of our results have applications in random matrix theory, a topic which we discuss in a separate (companion)…

This paper is divided into two independent parts. The first part presents new integral and series representations of the Riemaan zeta function. An equivalent formulation of the Riemann hypothesis is given and few results on this formulation…

We give a precise estimate of the Bergman kernel for the model domain defined by $\Omega_F=\{(z,w)\in \mathbb{C}^{n+1}:{\rm Im}w-|F(z)|^2>0\},$ where $F=(f_1,...,f_m)$ is a holomorphic map from $\mathbb{C}^n$ to $\mathbb{C}^m$, in terms of…

Helmke et al. have recently given a formula for the number of reachable pairs of matrices over a finite field. We give a new and elementary proof of the same formula by solving the equivalent problem of determining the number of so called…

In this paper, we give some results on closed polynomials and factorially closed polynomial in $n$ variables. In particular, we give a characterization of factorially closed polynomials in $n$ variables over an algebraically closed field…

Suppose that $\langle f_n \rangle$ is a sequence of polynomials, $\langle f_n^{(k)}(0)\rangle$ converges for every non-negative integer $k$, and that the limit is not $0$ for some $k$. It is shown that if all the zeros of $f_1, f_2, \dots$…

We shall give an explicit estimate of the lower bound of the Bergman kernel associated to a positive line bundle. In the compact Riemann surface case, our result can be seen as an explicit version of Tian's partial $C^0$-estimate.

We present an explicit formula for a weighted sum over the zeros of the Riemann zeta function. This weighted sum is evaluated in terms of a sum over the prime numbers, weighted with help of the Hermite polynomials. From the explicit formula…

There has been a great deal of work done in recent years on weighted Bergman spaces $\apa$ on the unit ball $\bn$ of $\cn$, where $0<p<\infty$ and $\alpha>-1$. We extend this study in a very natural way to the case where $\alpha$ is {\em…

We compute explicitly the Bergman kernels of all two dimensional monomial polyhedra, a class of domains including the Hartogs triangle and some of its generalizations. The kernel is computed from the representation of such domains as…

Building on the work of Arizmendi and Celestino (2021), we derive the $*$-distributions of polynomials in monotone independent and infinitesimally monotone independent elements. For non-zero complex numbers $\alpha$ and $\beta$, we derive…

In this article we study the field of Hilbertian metrics and positive definit (pd) kernels on probability measures, they have a real interest in kernel methods. Firstly we will make a study based on the Alpha-Beta-divergence to have a…

We prove the convergence of the normalized Fubini-Study measures and the logarithms of the Bergman kernels of various Bergman spaces of holomorphic and weakly holomorphic sections associated to a singular Hermitian holomorphic line bundle…

We introduce two classes of "egg type" domains, built on general bounded symmetric domains, for which we compute the Bergmann kernel in explicit form. We use the characterization of bounded symmetric domains through Jordan triple systems.…

The bicomplex Bergman spaces are studied for any bounded bicomplex domain. Its Bergman kernel is computed in terms of the kernels of the complex projections of the domain. We also introduce two additional reproducing kernel Hilbert spaces…

We propose a way to find the asymptotic distribution of zeros of orthogonal polynomials p_n(x) satisfying a difference equation of the form B(x)p_n(x+\delta)-C(x,n)p_n(x)+D(x)p_n(x-\delta)=0. We calculate the asymptotic distribution of…

The Bergman kernels of monomial polyhedra are explicitly computed. Monomial polyhedra are a class of bounded pseudoconvex Reinhardt domains defined as sublevel sets of Laurent monomials. Their kernels are rational functions and are obtained…

We study the probability distribution of the number of common zeros of a system of $m$ random $n$-variate polynomials over a finite commutative ring $R$. We compute the expected number of common zeros of a system of polynomials over $R$.…

We describe the limit zero distributions of sequences of polynomials with positive coefficients.