Weierstrass semigroup in towers of algebraic function fields

Althought many mathematicians have studied on the concepts of tower of algebraic function fields and Weierstrass semigroup, but up to now, there are not many paper about the behavior of the Weierstrass semigroup in a tower of function fields. In this thesis, the concept of tower of algebraic function fields, their properties over a finite field and the behaviour of Weierstrass semigroup H(P^{(m)}) at a rational point P, m≥0, are investigated. Moreover, for the purpose of calculating H(P^{(m)}) suitable and useful algorithms, methods are given for some families of tower of function fields defining special recursive equations.