Related papers: Rational 2-functions are abelian

We study a problem of Jeong and Taniguchi asking to find all rational maps which are Ahlfors functions. We prove that the rational Ahlfors functions of degree two are characterized by having positive residues at their poles. We then show…

We say that a formal power series $\sum a_n z^n$ with rational coefficients is a 2-function if the numerator of the fraction $a_{n/p}-p^2 a_n$ is divisible by $p^2$ for every prime number $p$. One can prove that 2-functions with rational…

We give defining equations for function fields over finite fields with many rational places. They are obtained from composita of quadratic extensions of the rational function field.

In this paper we deal with composite rational functions having zeros and poles forming consecutive elements of an arithmetic progression. We also correct a result published earlier related to composite rational functions having a fixed…

A rational function is the ratio of two complex polynomials in one variable without common roots. Its degree is the maximum of the degrees of the numerator and the denominator. Rational functions belong to the same class if one turns into…

Let $\Re_n$ be the set of all rational functions of the type $r(z) = p(z)/w(z),$ where $p(z)$ is a polynomial of degree at most $n$ and $w(z) = \prod_{j=1}^{n}(z-a_j)$, $|a_j|>1$ for $1\leq j\leq n$. In this paper, we set up some results…

We investigate semiconjugate rational functions, that is rational functions $A,$ $B$ related by the functional equation $A\circ X=X\circ B$, where $X$ is a rational function of degree at least two. We show that if $A$ and $B$ is a pair of…

We study the topological zeta function Z_{top,f}(s) associated to a polynomial f with complex coefficients. This is a rational function in one variable and we want to determine the numbers that can occur as a pole of some topological zeta…

In this paper, we establish some inequalities for rational functions with prescribed poles having s-fold zeros at origin and also show that it implies some inequalities for polynomials and their polar derivatives.

We single out some problems of Schubert calculus of subspaces of codimension 2 that have the property that all their solutions are real provided that the data are real. Our arguments explore the connection between subspaces of codimension 2…

In this article we consider rational functions on algebraic curves, which have one zero and one pole (and call pair of such function and curve Abel pair). We investigate moduli spaces of such functions on curves of genus one; the number of…

Abelian groups are classified by the existence of certain additive decompositions of group-valued functions of several variables with arity gap 2.

In this brief note, we consider p-adic unit roots or poles of L-functions of exponential sums defined over finite fields. In particular, we look at the number of unit roots or poles, and a congruence relation on the units. This raises a…

Let $c_1(x),c_2(x),f_1(x),f_2(x)$ be polynomials with rational coefficients. With obvious exceptions, there can be at most finitely many roots of unity among the zeros of the polynomials $c_1(x)f_1(x)^n+c_2(x)f_2(x)^n$ with $n=1,2\ldots$.…

A sequence of coefficients that appeared in the evaluation of a rational integral has been shown to be unimodal. An alternative proof is presented.

The bifurcation sets of polynomial functions have been studied by many mathematicians from various points of view. In particular, N\'emethi and Zaharia described them in terms of Newton polytopes. In this paper, we will show analogous…

Let f be a G-function (in the sense of Siegel), and x be an algebraic number; assume that the value f(x) is a real number. As a special case of a more general result, we show that f(x) can be written as g(1), where g is a G-function with…

We prove that if a linear equation, whose coefficients are continuous rational functions on a nonsingular real algebraic surface, has a continuous solution, then it also has a continuous rational solution. This is known to fail in higher…

We present criteria for deciding whether a bivariate rational function in two variables can be written as a sum of two (q-)differences of bivariate rational functions. Using these criteria, we show how certain double sums can be evaluated,…

To an ideal in $\mathbb{C}[x,y]$ one can associate a topological zeta function. This is an extension of the topological zeta function associated to one polynomial. But in this case we use a principalization of the ideal instead of an…