Related papers: A functional equation for monomial functions

The aim of this sequence of work is to investigate polynomial equations satisfied by additive functions. As a result of this, new characterization theorems for homomorphisms and derivations can be given. More exactly, in this paper the…

Given a cardinal $\kappa$ that is $\lambda$-supercompact for some regular cardinal $\lambda\geq\kappa$ and assuming $\GCH$, we show that one can force the continuum function to agree with any function $F:[\kappa,\lambda]\cap\REG\to\CARD$…

Let kappa be an uncountable regular cardinal. Call an equivalence relation on functions from kappa into 2 Sigma_1^1-definable over H(kappa) if there is a first order sentence F and a parameter R subseteq H(kappa) such that functions…

We prove that the graph of a discontinuous $n$-monomial function $f:\mathbb{R}\to\mathbb{R}$ is either connected or totally disconnected. Furthermore, the discontinuous monomial functions with connected graph are characterized as those…

Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…

Classical planar functions are functions from a finite field to itself and give rise to finite projective planes. They exist however only for fields of odd characteristic. We study their natural counterparts in characteristic two, which we…

In this paper, we give some results on closed polynomials and factorially closed polynomial in $n$ variables. In particular, we give a characterization of factorially closed polynomials in $n$ variables over an algebraically closed field…

Let $k$ be an algebraically closed field of characteristic zero, and $k[[z]]$ the ring of formal power series over $k$. In this paper, we study equations in the semigroup $z^2k[[z]]$ with the semigroup operation being composition. We prove…

For a generic value of the central charge, we prove the holomorphic factorization of partition functions for free superconformal fields which are defined on a compact Riemann surface without boundary. The partition functions are viewed as…

Let $f$ be a transcendental meromorphic function defined in the complex plane $\mathbb{C}$, and $\varphi(\not\equiv 0,\infty)$ be a small function of $f$. In this paper, We give a quantitative estimation of the characteristic function $T(r,…

Let $\mathbb{K}$ be an uncountable field of characteristic zero and let $f$ be a function from $\mathbb{K}^n$ to $\mathbb{K}$. We show that if the restriction of $f$ to every affine plane $L\subset\mathbb{K}^n$ is regular, then $f$ is a…

Let $p$ be an odd prime and $\F_q$ be the finite field with $q=p^n$ elements. A planar function $f:\F_q\rightarrow\F_q$ is called homogenous if $f(\lambda x)=\lambda^df(x)$ for all $\lambda\in\F_p$ and $x\in\F_q$, where $d$ is some fixed…

Let $\mathbb{F}_q$ be a finite field with $q$ elements and let $n$ be a positive integer. In this paper, we study the digraph associated to the map $x\mapsto x^n h(x^{\frac{q-1}{m}})$, where $h(x)\in\mathbb{F}_q[x].$ We completely determine…

A function $\mathfrak{F}$ with simple and nice algebraic properties is defined on a subset of the space of complex sequences. Some special functions are expressible in terms of $\mathfrak{F}$, first of all the Bessel functions of first…

Let $(G,+)$ be a topological abelian group with a neutral element $e$ and let $\mu : G\longrightarrow\mathbb{C}$ be a continuous character of $G$. Let $(\mathcal{H}, \langle \cdot,\cdot \rangle)$ be a complex Hilbert space and let…

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…

One of the goals of the present paper is to propose an elementary method to find a general formula for the Fourier transform containing a pair of complex gamma functions with a monomial sm in terms of Gauss's hypergeometric functions 2F1.…

Using Stickelberger's theorem on Gauss sums, we show that if $F$ is a planar function on a finite field $\mathbb{F}_q$, then for all non-zero functions $G : \mathbb{F}_q \to \mathbb{F}_q$, we have \begin{equation*} d_{\mathsf{alg}}(G \circ…

We study CAT(kappa) spaces X admitting affine functions. We show that there exists a canonical isometric embedding X -> Y x H where H is a Hilbert space, such that every affine function f: X -> R factors as f'o p, where p is the projection…

We investigate the finitary functions from a finite product of finite fields $\prod_{j =1}^m\mathbb{F}_{q_j} = \mathbb{K}$ to a finite product of finite fields $\prod_{i =1}^n\mathbb{F}_{p_i} = \mathbb{F}$, where $|\mathbb{K}|$ and…