Analytic Number Theory
(dt. Analytische Zahlentheorie)
|Level, degree of commitment in original study programme||Advanced module, compulsory elective module|
|Forms of teaching and learning,
|Lecture (4 SWS), recitation class (2 SWS), |
270 hours (90 h attendance, 180 h private study)
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
|German,The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.|
|Original study programme||M.Sc. Mathematik / Vertiefungsbereich Mathematik|
|One semester, |
Regelmäßig im Wechsel mit anderen advanced moduleen in Algebra oder Analysis
|Person in charge of the module's outline||Prof. Dr. Pablo Ramacher|
- Arithmetic functions and Dirichlet series,
- Characters and summation formulas,
- L-functions and Riemann's zeta-function,
- Exponential sums and Dirichlet polynomials,
- Sieve methods and applications of the Large Sieve,
- Equidistribution results for prime numbers in residual classes,
- holomorphic automorphic functions.
The students shall
- learn to transfer, develop and apply analytic methods to number theoretical questions,
- train analytical ways of thinking and working,
- learn modern techniques for scientific work in this field,
- practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
- improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.
None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Complex Analysis and Vector Analysis, Number Theory.
- Brüdern, J.: Einführung in die analytische Zahlentheorie, Springer.
- Davenport, H.: Multiplicative Number Theory, Springer.
- Iwaniec, H.: Analytic number theory, AMS Colloquium Publications.
This page describes a module according to the latest valid module guide in Sommersemester 2021. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:
- WiSe 2016/17 (no corresponding element)
- SoSe 2018 (no corresponding element)
- WiSe 2018/19
- WiSe 2019/20
- WiSe 2020/21
- SoSe 2021
- WiSe 2021/22
The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.
The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.