Number theory [ LMAT2440 ]
5.0 crédits ECTS
30.0 h + 15.0 h
1q
| Teacher(s) |
Caprace Pierre-Emmanuel ;
|
| Language |
French
|
Place
of the course |
Louvain-la-Neuve
|
| 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.
|
| 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.
|
Cycle et année
d'étude |
> Master [120] in Mathematics
> Master [60] in Mathematics
> Master [120] in Computer Science and Engineering
> Master [120] in Mathematical Engineering
> Master [120] in Electrical Engineering
|
Faculty or entity
in charge |
> MATH
|
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