Analytic Algebraic Number Theory

Master course (Fall 2019) – Universität Basel
Lecturer: Pierre Le Boudec
Assistant: Richard Griffon

Website Vorlesungverzeichnis (Lecture)
Vorlesungverzeichnis (Exercises)
Exercise classes Thursdays 8:15am – 10:00am
Spiegelgasse 5, Seminarraum 05.001
Exercise sheets

Exercise sheets are also posted on the ADAM page for the course.

Sheet # Date Topics Homework due
1 Sept. 23 Finite fields, Euclidean rings, PID, UFD ... Sept. 30
2 Sept. 30 Modules over $\mathbb{Z}$, Quadratic number fields, Traces and norms, ... Oct. 7
3 Oct. 7 Discriminant, Noetherian modules, Gaussian integers and a Diophantine equation, ... Oct. 14
4 Oct. 14 Eisenstein's criterion, Cyclotomic polynomials, Integers in cyclotomic fields, ... Oct. 21
5 Oct. 21 Hermite's theorem, Determination of a ring of integers, Class numbers of some quadratic fields, ... Oct. 28
6 Oct. 28 A bound on the class number, Units in real quadratic fields, localisation of ideals, ... Nov. 4
7 Nov. 4 Dedekind-Kummer on decomposition of primes, Splitting of primes in quadratic fields, ... Nov. 11
8 Nov. 11 Decomposition and inertia groups, Quadratic Reciprocity Law, a Fermat-Pell equation, ... Nov. 18
9 Nov. 18 Rabinowitz's theorem, Hyperbola method, Quadratic Gauss sums, ... Nov. 25
10 Nov. 25
Others
• Notes on modules over a PID (Sept. 26).
E-mail richard.griffon@unibas.ch