Number theory [ LMAT2440 ]

5.0 crédits ECTS 30.0 h + 15.0 h 1q > Schedule

Teacher(s)	Quisquater Jean-Jacques ;
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 and year of study	> Master in Mathematics > Deuxième année de master [120] : ingénieur civil électricien, à finalité spécialisée > Première année de master [120] en sciences informatiques à finalité spécialisée
Faculty or entity in charge	> MATH