Related papers: Radially distributed values and normal families, I…
For families of smooth complex projective varieties we show that normal functions arising from algebraically trivial cycle classes are algebraic, and defined over the field of definition of the family. In particular, the zero loci of those…
The spectrum of two-point functions in a holographic renormalization group flow from an ultraviolet (UV) to an infrared (IR) conformal fixed point is necessarily continuous. For a toy model, the spectral function does not only show the…
We study a new orthogonal family of $L$-functions associated with holomorphic Hecke newforms of level $q$, averaged over $q \asymp Q$. To illustrate our methods, we prove a one level density result for this family with the support of the…
We consider the set of Baire 1 functions endowed with the pointwise partial ordering and investigate the structure of the linearly ordered subsets.
We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically and explicit…
We consider a class $\THO$ of typically real harmonic functions on the unit disk that contains the class of normalized analytic and typically real functions. We also obtain some partial results about the region of univalence for this class.
A heuristic principle attributed to A. Bloch says that a family of holomorphic functions is likely to be normal if there is no nonconstant entire functions with this property. We discuss this principle and survey recent results that have…
We study the fluctuations in the distribution of zeros of zeta functions of a family of hyperelliptic curves defined over a fixed finite field, in the limit of large genus. According to the Riemann Hypothesis for curves, the zeros all lie…
Let $M$ be a subharmonic function on a domain $D$ in the complex plane $\mathbb C$ with the Riesz measure $\nu_M$. Let $f$ be a non-zero holomorphic function on $D$ such that $\log |f|\leq M$ on $D$ and the function $f$ vanish on a sequence…
Normal distribution manifolds play essential roles in the theory of information geometry, so do holonomy groups in classification of Riemannian manifolds. After some necessary preliminaries on information geometry and holonomy groups, it is…
We describe symmetric diffusion operators where the spectral decomposition is given through a family of orthogonal polynomials. In dimension one, this reduces to the case of Hermite, Laguerre and Jacobi polynomials. In higher dimension,…
We study the map associating the cohomology class of an admissible normal function on the product of punctured disks, and give some sufficient conditions for the surjectivity of the map. We also construct some examples such that the map is…
In this paper we relate the location of the complex zeros of the reliability polynomial to parameters at which a certain family of rational functions derived from the reliability polynomial exhibits chaotic behaviour. We use this connection…
We compare the Riemann $\Xi$--function to a canonical real-entire reference family arising from the cycle Laplacian developed in Paper I. These spectral determinants have only real zeros by self-adjointness. Our main tool is a rigidity…
We study radial behavior of harmonic functions in the unit disk belonging to the Korenblum class. We prove that functions which admit two-sided Korenblum estimate either oscillate or have slow growth along almost all radii.
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…
We consider the family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2z^2+a_3z^3+\cdots$. Our objective in this paper is to estimate the difference of the moduli of successive coefficients, that is $\big |…
We consider the class univalent log-harmonic mappings on the unit disk. Firstly, we obtain necessary and sufficient conditions for a complex-valued continuous function to be starlike or convex in the unit disk. Then we present a general…
We generalize the concept of localization of a star operation to flat overrings; subsequently, we investigate the possibility of representing the set $\mathrm{Star}(R)$ of star operations on $R$ as the product of $\mathrm{Star}(T)$, as $T$…
We study nonlinear resolvents of holomorphic generators of one-parameter semigroups acting in the open unit disk. The class of nonlinear resolvents can be studied in the framework of geometric function theory because it consists of…