Vorlesungverzeichnis (Exercises)
Spiegelgasse 5, Seminarraum 05.001
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 | The Gamma function (Wielandt's theorem and reflexion formula), Primes in arithmetic progression, Perron's formula, ... | Dec. 2 |
| 11 | |
Dec. 2 | Use of Perron's formula, Explicit zeta functions of quadratic fields, Fourier transform of Gaussians, ... | Dec. 9 |
| 12 | |
Dec. 10 | Bauer's theorem, Computation of $L(\chi, 1)$, Different, ... | Dec. 17 |
- Notes on modules over a PID (Sept. 26).