Explicit methods in algebraic number theory | Doctoral School of Mathematical and Computational Sciences

Leader: Prof. Dr. István Gaál, full professor

Introduction to algebraic number theory. Theory of valuations. Finite fields, cyclotomic fields, Galois theory. Algorithms for solving diophantine equations. Algorithms in algebraic number theory. Lattices, basis reduction methods and applications. Combinatorial methods in number theory. Program packages in algebraic number theory. Arithmetical properties of modular forms. Units and unit equations. Elliptic curves and their applications.