Related papers: Zeros of new Bergman kernels

In this article, we study some properties of the $n$-th order weighted reduced Bergman kernels for planar domains, $n\geq 1$. Specifically, we look at Ramadanov type theorems, localization, and boundary behaviour of the weighted reduced…

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…

The complex or non-hermitian orthogonal polynomials with analytic weights are ubiquitous in several areas such as approximation theory, random matrix models, theoretical physics and in numerical analysis, to mention a few. Due to the…

Let $\mathbb{Q}(\alpha)$ and $\mathbb{Q}(\beta)$ be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, $\mathbb{Q}(\beta) \rightarrow \mathbb{Q}(\alpha)$. The algorithm is particularly efficient if…

Given a sequence of positive Hermitian holomorphic line bundles $(L_p,h_p)$ on a K\"ahler manifold $X$, we establish the asymptotic expansion of the Bergman kernel of the space of global holomorphic sections of $L_p$, under a natural…

In this note, we prove a central limit theorem for smooth linear statistics of zeros of random polynomials which are linear combinations of orthogonal polynomials with iid standard complex Gaussian coefficients. Along the way, we obtain…

In this paper we investigate distribution of zeros for only quasipolynom and obtain exactly lower-bound for their modulus.

We investigate completed interlacing of zeros for pairs of polynomial sequences that fail to interlace by exactly two points. Using a general mixed recurrence relation, we identify a quadratic polynomial whose zeros serve as the two extra…

This is partly a survey article for Constructive Approximation's Special Issue on Approximation and Statistical Physics. It reviews results of B. Shiffman-S.Zelditch, R. Berman. S. Boucksom, D. Witt-Nystrom, T. Bloom, O. Zeitouni and others…

Locating the zeros of quaternionic polynomials is a fundamental problem with significant implications across scientific and engineering disciplines, yet the noncommutative nature of quaternion multiplication makes it fundamentally more…

We present a technique for computing explicit, concrete formulas for the weighted Bergman kernel on a planar domain with weight the modulus squared of a meromorphic function in the case that the meromorphic function has a finite number of…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

We explore the relationship between the Bergman kernel of a Hartogs domain and weighted Bergman kernels over its base domain. In particular we develop a representation of the Bergman kernel of a Hartogs domain as a series involving weighted…

Actually we will discuss some topics related to Bergman kernel on Cartan- Hartogs domain.

A quantum mechanical search procedure to determine the real zeros of a polynomial is introduced. It is based on the construction of a spin observable whose eigenvalues coincide with the zeros of the polynomial. Subsequent quantum mechanical…

We obtain the octonionic Bergman kernel for half space in the octonionic analysis setting by two different methods. As a consequence, we unify the kernel forms in both complex analysis and hyper-complex analysis.

In this work we prove an universality result regarding the equidistribution of zeros of random holomorphic sections associated to a sequence of singular Hermitian holomorphic line bundles on a compact K\"ahler complex space $X$. Namely,…

We investigate the interlacing of zeros of polynomials of different degrees within the sequences of $q$-Laguerre polynomials $\left\{\tilde{L}_n^{(\delta)}(z;q)\right\}_{n=0}^{\infty}$ characterized by $\delta\in(-2,-1).$ The interlacing of…

Let $K = \mathbb{Q}(\zeta_3)$, where $\zeta_3$ is a primitive root of unity. In this paper we study the distribution of integers $\alpha \in \mathcal{O}_K$ for which the norm equation $N_{K(\sqrt[3]{\alpha})/K}(\mathbf{x}) = \zeta_3$ is…

In this paper we provide properties -- which are, to the best of our knowledge, new -- of the zeros of the polynomials belonging to the q-Askey scheme. These findings include Diophantine relations satisfied by these zeros when the…