UCL - Number theory

[MAT2440]

[30h + 15h] 5 credits

This course is taught in the 1st semester.

Teacher(s): Jean-Jacques Quisquater, Jean-Pierre Tignol

Language: French

Level: Second

Aims
Main themes

Aims

This course provides the concepts and methods needed for : - solving equations in rings of modular integers ;- finding conditions for the solvability of some Diophantine equations ;- applying theorems of analysis to the study of prime numbers ;- computing in the group of points of some projective cubics.

Main themes

Introduction to various aspects of number theory, with an emphasis on applications to cryptography.1. Modular arithmetic : the Chinese remainder theorem and the law of quadratic reciprocity.2. Rational quadratic forms : the field of p-adic numbers and the Hasse local-global principle.3. Analytical number theory : zeta function and the Dirichlet theorem.4. Projective cubics ; arithmetical properties of elliptic curves.The balance between the topics above may vary from one year to another.Teaching style : theoretical talks.