In the article, we prove that the double inequality [Formula: see text] holds for all [Formula: see text], we present the best possible constants λ and μ such that [Formula: see text] for all [Formula: see text], and we find the value of [Formula: see text] in the interval [Formula: see text] such that [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text], ...

Fix a nontrivial interval X C R and let / e C1(X,X) be a chaotic mapping. We denote by Aoo (/) the set of points whose orbits do not converge to a (one-sided) asymptotically stable periodic orbit of / or to a subset of the absorbing boundary of X for /. A. We assume that / satisfies the following conditions: (1) the set of asymptotically stable periodic points for / is compact (an empty set is ...

Using functional properties of the Hurwitz zeta function and symbolic derivatives of the trigonometric functions, the function ζ(2n + 1, p/q) is expressed in several ways in terms of other mathematical functions and numbers, including in particular the Glaisher numbers. 2000 Mathematics Subject Classification. Primary 11M35, 33B99. Secondary 11B75, 33E20.

We study the Gross Conjecture on the cyclotomic function field extension k(Λf )/k where k = Fq(t) is the rational function field and f is a monic polynomial in Fq[t]. We show the conjecture in the Fermat curve case(i.e., when f = t(t− 1)) by direct calculation. We also prove the case when f is irreducible which is analogous to Weil’s reciprocity law. In the general case, we manage to show the w...

Let K be a number field, and let f ∈ K(x) be a nonconstant rational function. We study the sets { n ∑ i=1 f(xi) : xi ∈ K − {poles of f} }

This paper presents a polynomial time algorithm for determining when a univariate rational function is the composition of two rational functions, and, if so, nds those rational functions. This algorithm is valid for rational functions over arbitrary elds and thus also resolves an outstanding problem: polynomial decomposition over elds of nite characteristic. In addition, we present a framework ...

Abramov’s algorithm enables us to decide whether a univariate rational function can be written as a difference of another rational function, which has been a fundamental algorithm for rational summation. In 2014, Chen and Singer generalized Abramov’s algorithm to the case of rational functions in two (q-)discrete variables. In this paper we solve the remaining three mixed cases, which completes...