Related papers: Zero-free regions for Dirichlet series (II)
We introduce certain special polynomials in an arbitrary number of indeterminates over a finite field. These polynomials generalize the special polynomials associated to the Goss zeta function and Goss-Dirichlet $L$-functions over the ring…
We discuss a special class of solutions to the minimal surface system. These are vector-valued functions that "decrease area" and are natural generalization of scalar functions. After defining area-decreasing maps, we show several classical…
Necessary and sufficient conditions for the interlacing of the zeros of cylinder functions and their derivatives of different orders are given.
We announce a scale of Blaschke-type conditions for subsequences of zeros of holomorphic functions on arbitrary domains in the extended complex plane.
Spectral zeta functions $\zeta(s)$ for the massless scalar fields obeying the Dirichlet and Neumann boundary conditions on a surface of an infinite cylinder are constructed. These functions are defined explicitly in a finite domain of the…
We consider the interpretation in classical geometry of conformal field theories constructed from orbifolds with discrete torsion. In examples we can analyze, these spacetimes contain ``stringy regions'' that from a classical point of view…
A new method to extract the density of partition function zeroes (a continuous function) from their distribution for finite lattices (a discrete data set) is presented. This allows direct determination of the order and strength of phase…
We investigate the zeros of two one-parameter families of harmonic functions and describe how the number of zeros depends on the parameter. Our functions have the property that all zeros lie on certain rays in the complex plane and thus we…
We give a description of the intersection of the zero set with the unit sphere of a zero-free polynomial in the unit ball of $\mathbb{C}^n$. This description leads to the formulation of a conjecture regarding the characterization of…
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…
We obtain various general conditions in terms of the balayage and Green's functions under which the sequence of points is the zero set for weighted spaces of holomorphic functions in a domain on the complex plane.
On negatively curved compact manifolds, it is possible to associate to every closed form a bounded cocycle - hence a bounded cohomology class - via integration over straight simplices. The kernel of this map is contained in the space of…
We investigate simpliciality of function spaces without constants. We prove, in particular, that several properties characterizing simpliciality in the classical case differ in this new setting. We also show that it may happen that a given…
We derive a general formula for the product of two Dirichlet series that satisfy Hecke's functional equation. Several examples are provided to demonstrate the applicability of the formula. In addition, we discuss prior work on similar…
We show the zero-density estimate \[ N(\zeta_{\mathcal{P}}; \alpha, T) \ll T^{\frac{4(1-\alpha)}{3-2\alpha-\theta}}(\log T)^{9} \] for Beurling zeta functions $\zeta_{\mathcal{P}}$ attached to Beurling generalized number systems with…
We propose a notion of minimal free resolutions for differential modules, and we prove existence and uniqueness results for such resolutions. We also take the first steps toward studying the structure of minimal free resolutions of…
We consider massless Dirac operators on the real line with compactly supported potentials. We solve two inverse problems (including characterization): in terms of zeros of reflection coefficient and in terms of poles of reflection…
We initiate the study of fine $p$-(super)minimizers, associated with $p$-harmonic functions, on finely open sets in metric spaces, where $1 < p < \infty$. After having developed their basic theory, we obtain the $p$-fine continuity of the…
We give explicit real-analytic functions whose zero sets characterize the images of the standard maps of wave-front singularities. Such functions are realizations of the main-analytic sets in the sense of Ishikawa-Koike-Shiota (1984). More…
We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free. In particular, we characterize all homogeneous isosceles-free spaces up to…