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401-3100-71L 4 Credits BSC , MSC D-MATH

Student Seminar in Number Theory: L-Functions

Lecturers & Examiners: Dr. Markus Schwagenscheidt
Number of participants limited to 24.
VVZ CR n/a

Last Updated: 2026-02-05 15:47:29

Abstract

Seminar on the basic theory of Dirichlet L-functions and some applications in number theory.

Objective

In the seminar we will study Dirichlet L-functions, which generalize the classical Riemann zeta function. We discuss their basic properties, such as the analytic continuation and the functional equation, and the rationality of some of their special values. Moreover, we investigate the connection of Dirichlet L-functions with the Dedekind zeta functions of quadratic number fields. As main applications, we prove Dirichlet's class number formula for quadratic fields and Dirichlet's Theorem on arithmetic progressions. We follow the book of Don Zagier "Zetafunktionen und quadratische Körper"

Content

Please see the website of the seminar for a list of topics: https://people.math.ethz.ch/~mschwagen/lfunctions

Resources

Literature

Apostol - Introduction to analytic number theory Davenport - Multiplicative number theory Serre - A course in arithmetic Zagier - Zetafunktionen und quadratische Körper

General Information

Language
English
Levels
BSC , MSC

Examination

Type
ungraded semester performance

Registration & Places

Limited places (Special selection)
Signup Start
02.08.2021
Signup End
17.09.2021
Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
seminar Student Seminar in Number Theory: L-Functions
  • Tue 12:15-14:00 (HG F 26.5)
2 h weekly

Offered In

  • Mathematics Bachelor
    • Seminars (NOTICE: The number of seminar places is limited, and the special selection procedure should help to allocate the places not primarily according to the registration time. Everybody is waitlisted first when he/she tries to register for a seminar in myStudies. Moreover: Only one mathematics seminar can be chosen per semester.)
  • Mathematics Master
    • Seminars and Semester Papers
      • Seminars (NOTICE: The number of seminar places is limited, and the special selection procedure should help to allocate the places not primarily according to the registration time. Everybody is waitlisted first when he/she tries to register for a seminar in myStudies. Moreover: Only one mathematics seminar can be chosen per semester. In case you need to attend 2 seminars in this semester, please take contact with the Study Administration (email: ).)