On certain transcendental numbers.

On Transcendental Numbers

Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them. New inequalities for transcendental numbers are stated in Section 2 and proved in Section 4. Also, in relationship with these topics, we study the exponential function axioms related to the Yang-Baxter equation.

Dedekind Sums with Arguments near Certain Transcendental Numbers

We study the asymptotic behavior of the classical Dedekind sums s(sk/tk) for the sequence of convergents sk/tk k ≥ 0, of the transcendental number

On Irrational and Transcendental Numbers

Algebraic and Transcendental Numbers

To begin with, recall that a complex number α is said to be a root of a polynomial P (X) if P (α) = 0. A complex number α is said to be algebraic if there is a nonzero polynomial P (X), with integer coefficients, of which α is a root. The set of algebraic numbers is denoted by Q̄. A complex number α which is not algebraic is said to be transcendental. The following numbers are obviously algebrai...

Algebraic Dynamics and Transcendental Numbers

A first example of a connection between transcendental numbers and complex dynamics is the following. Let p and q be polynomials with complex coefficients of the same degree. A classical result of Böttcher states that p and q are locally conjugates in a neighborhood of∞: there exists a function f , conformal in a neighborhood of infinity, such that f(p(z)) = q(f(z)). Under suitable assumptions,...