Related papers: Zero-free regions for Dirichlet series (II)
Motivated by existing blend-to-zero techniques, a formal framework is developed for defining and constructing blend-to-zero operators on closed intervals for the generation of sufficiently smooth transitions between functions. Such…
We study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are…
We establish many previously unknown properties of zero-divisors in Cayley-Dickson algebras. The basic approach is to use a certain splitting that simplifies computations surprisingly.
In this paper we characterize the zero sets of functions from $\ell^{p}_{A}$ (the analytic functions on the open unit disk $D$ whose Taylor coefficients form an $\ell^p$ sequence) by developing a concept of an "inner function" modeled by…
Inspired by a recent article on Fr\'echet spaces of ordinary Dirichlet series $\sum a_n n^{-s}$ due to J.~Bonet, we study topological and geometrical properties of certain scales of Fr\'echet spaces of general Dirichlet spaces $\sum a_n…
Correlation functions can be calculated on Riemann surfaces using the operator formalism. The state in the Hilbert space of the free field theory on the punctured disc, corresponding to the Riemann surface, is constructed at infinite genus,…
Let $K$ be a number field and, for an integral ideal $\mathfrak{q}$ of $K$, let $\chi$ be a character of the narrow ray class group modulo $\mathfrak{q}$. We establish various new and improved explicit results, with effective dependence on…
The positions of poles and zeros of a filter circuit indicates how the system behaves with variation in frequency as well as it results a tool to utilize the system gain by setting the frequency range in a complex process. The existing…
In the article "Picard-Vessiot theory of differentially simple rings" we established a Picard-Vessiot theory over differentially simple rings which may not be fields. Differential modules over such rings were proven to be locally free but…
The paper has two parts. First we prove that the specialization maps on R-equivalence and on the Chow group of zero cycles are isomorphisms for families over a local, Henselian, Dedekind ring when the special fiber is smooth and separably…
We give a complete description of zero sets for some well-known subclasses of entire functions of exponential growth (bounded on real axis, Cartwright's class)
This paper improves the upper bound for the exceptional zeroes of Dirichlet L-functions with even characters. The result is obtained by improving on explicit estimate for $L'(\sigma;\chi)$ for $\sigma$ close to unity, using a result on the…
We consider transcendental entire functions of finite order for which the zeros and $1$-points are in disjoint sectors. Under suitable hypotheses on the sizes of these sectors we show that such functions must have a specific form, or that…
This paper deals with the problem of describing the vector spaces of divergence-free, natural tensors on a pseudo-Riemannian manifold that are second-order; i.e., that are defined using only second derivatives of the metric. The main result…
Consider a given space, e.g., the Euclidean plane, and its decomposition into Voronoi regions induced by given sites. It seems intuitively clear that each point in the space belongs to at least one of the regions, i.e., no neutral region…
We prove joint universality theorems on the half plane of absolute convergence for general classes of Dirichlet series with an Euler-product, where in addition to vertical shifts we also allow scaling. This generalizes our recent joint…
We associate a graph to a possible non-zero zero-divisor in the group algebra of a torsion-free group.
A method of constructing an entire function with given zeros and estimates of growth is suggested. It gives a possibility to describe zero sets of certain classes of entire functions of one and several variables in terms of growth of volume…
In a previous paper, Yakubovich and the author of this article proved that certain shifted combinations of completed Dirichlet series have infinitely many zeros on the critical line. Here we provide some lower bounds for the number of…
We describe in detail three distinct families of generalized zeta functions built over the (nontrivial) zeros of a rather general arithmetic zeta or L-function, extending the scope of two earlier works that treated the Riemann zeros only.…