Course overview

This course is intended to give its participants a more profound knowledge of both algebra and number theory, and to supply the foundations of further independent scientific study in this direction. It will treat the following themes, among others:

• Algebraic number fields
• Finiteness of the class number
• Dirichlet's unit theorem
• Zeta- and L-functions
• Explicit aspects

Prerequisites

• Elemente der Algebra
• Elemente der Funktionentheorie

Target audience and examination

This is a V4Ue2 course that counts for 9LP. It will be given in English.

Bachelor

In the Bachelor, this course is not yet examined. However, it can be followed as an additional module.

Master

In the Master Mathematics and Mathematical Economics, this course can be taken as a chosen compulsory module in Pure Mathematics.

• Neukirch, J.: Algebraische Zahlentheorie, Springer
• Milne, J.: Algebraic Number Theory
• Stein, W.: Algebraic Number Theory, a Computational Approach
• Stevenhagen, P.: Number Rings
• Wewers, S.: Algebraic Number Theory
• Sijsling, J.: Algebraic Number Theory (Vorlesungsskript)