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This entry is from Winter semester 2019/20 and might be obsolete. You can find a current equivalent here.

Analytic Number Theory
(dt. Analytische Zahlentheorie)

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements		 9 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
Duration,
frequency		 One semester,
Regularly alternating with other specialization modules in Algebra or Analysis
Person in charge of the module's outline Prof. Dr. Pablo Ramacher

Contents

  • 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.

Qualification Goals

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.

Prerequisites

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.


Applicability

Module imported from M.Sc. Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • LAaG Mathematics

When studying M.Sc. Computer Science, this module can be attended in the study area Minor subject Mathematics.


Recommended Reading

  • Brüdern, J.: Einführung in die analytische Zahlentheorie, Springer.
  • Davenport, H.: Multiplicative Number Theory, Springer.
  • Iwaniec, H.: Analytic number theory, AMS Colloquium Publications.



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2019/20. 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:

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.