Class Field Theory and Elliptic Curves with Complex Multiplication

openClass field theory is a branch of algebraic number theory which has the purpose of studying and classifying abelian extensions of fields. The work starts with a detailed study of this theory based on a cohomological approach which leads to the statements and the proofs of the main theorems both in the local and global cases. Then, after a brief introduction on elliptic curves with complex multiplication, the main goal of the thesis is to study their relation with class field theory in the particular case of quadratic imaginary fields.Class field theory is a branch of algebraic number theory which has the purpose of studying and classifying abelian extensions of fields. The work starts with a detailed study of this theory based on a cohomological approach which leads to the statements and the proofs of the main theorems both in the local and global cases. Then, after a brief introduction on elliptic curves with complex multiplication, the main goal of the thesis is to study their relation with class field theory in the particular case of quadratic imaginary fields

Error Bounds of Gaussian Quadratures for One Class of Bernstein-Szego Weight Functions

We consider the action of the automorphism group I(n) of Zn on the set of k−sets of Zn in the natural way. Although elementary in its nature, it has not been fully analyzed and understood yet. The vast class of enumerative and computational problems problems is related to this action. For example, the number of orbits on the set of k−sets of Zn is one of them that we are interested in. Those enumerative problems are mainly resolved by application of P olya's theory

Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education

International audienceThis volume contains the Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (ERME), which took place 9-13 February 2011, at Rzeszñw in Poland