Related papers: The Lemniscatic Functions
We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…
We explicitly evaluate a special type of multiple Dirichlet $L$-values at positive integers in two different ways: One approach involves using symmetric functions, while the other involves using a generating function of the values. Equating…
We strengthen certain known results saying that separately regular functions are rational and separately Nash functions are semialgebraic. The approach presented here unifies and highlights the similarities between the two problems.
The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is…
We establish the universality theorem for the first four symmetric power L-functions of automorphic forms and their associated Rankin-Selberg L-functions. This generalizes some results of Laurincikas & Matsumoto and Matsumoto respectively.
This article studies the Galois groups that arise from division points of the lemniscate. We compute these Galois groups two ways: first, by class field theory, and second, by proving the irreducibility of lemnatomic polynomials, which are…
The object of the present paper is to study of two certain subclass of analytic functions related with Booth lemniscate which we denote by $\mathcal{BS}(\alpha)$ and $\mathcal{BK}(\alpha)$. Some properties of these subclasses are…
Necessary and sufficient conditions for Lipschitzness of the Lempert and Green functions are found in terms of their boundary behaviors.
The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…
In this paper, by making use of properties of elliptic functions, we describe meromorphic solutions of Fermat-type functional equations $f(z)^{n}+f(L(z))^{m}=1$ over the complex plane $\mathbb{C}$, where $L(z)$ is a nonconstant entire…
The addition of certain nonrenormalizable terms to the usual action density of a free scalar field leads to nonrenormalizable theories whose exact euclidian and minkowskian Green's functions are less singular than those of the free theory.…
Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic…
We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two…
An introduction to geometric valuation theory is given. The focus is on classification results for $\operatorname{SL}(n)$ invariant and rigid motion invariant valuations on convex bodies and on convex functions.
We review some aspects of the theory of spherical Bessel functions and Struve functions by means of an operational procedure essentially of umbral nature, capable of providing the straightforward evaluation of their definite integrals and…
A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Applying the generators of the closed subalgebra generated by…
In this note, we study polynomial and rational lemniscates as trajectories of related quadratic differentials. Many classic results can be then proved easily...
We introduce first weighted function spaces on Rd using the Dunkl convolution that we call Besov-Dunkl spaces. We provide characterizations of these spaces by decomposition of functions. Next we obtain in the real line and in radial case on…
We propose dynamical systems defined on algebra of lattices, which we call `lattice equations'. We give exact general solutions of initial value problems for a class of lattice equations, and evaluate the complexity of the solutions.…