We present a method of Zariski-van Kampen type for the calculation of the transcendental lattice of a complex projective surface. As an application, we calculate the transcendental lattices of complex singular K3 surfaces associated with an arithmetic Zariski pair of maximizing sextics of type A10 + A9 that are defined over Q( √ 5) and are conjugate to each other by the action of Gal(Q( √

This paper is devoted to establish sufficient conditions under which a transcendental meromorphic function has no unbounded Fatou components and to extend some results for entire functions to meromorphic function. Actually, we shall mainly discuss non-existence of unbounded wandering domains of a meromorphic function. The case for a composition of finitely many meromorphic function with at leas...

This paper presents a decision procedure for a certain class of sentences of first order logic involving integral polynomials and a certain specific analytic transcendental function trans(x) in which the variables range over the real numbers. The list of transcendental functions to which our decision method directly applies includes exp(x), the exponential function with respect to base e, ln(x)...

Yair Minsky showed that punctured torus groups are classified by a pair of ending laminations (ν − , ν+). In this note, we show that there are ending laminations ν+ such that for any choice of ν − , the punctured torus group is transcendental as a subgroup of PSL2C.

How come that finite language can produce certainty — at least a sufficiently certain certainty, sometimes apodictic — in the presence of infinity? The answer can by no means be found in external reality, quite the contrary: it seems that the very purpose of semantics is to make this question untractable with the help of an ad hoc analytical newspeak in which one cannot even formulate the above...

The aim of this paper is to exhibit a method for proving that certain analytic functions are not solutions of algebraic differential equations. The method is based on model-theoretic properties of differential fields and properties of certain known transcendental differential functions, as of Γ(x). Furthermore, it also determines differential transcendency of solution of some functional equatio...