Universität Wien

250104 VO Analytic Number Theory (2005W)

Analytic Number Theory

0.00 ECTS (4.00 SWS), SPL 25 - Mathematik

erstmals ab 04.10.2005

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 04.10. 15:00 - 17:00 Seminarraum
  • Thursday 06.10. 15:00 - 17:00 Seminarraum
  • Tuesday 11.10. 15:00 - 17:00 Seminarraum
  • Thursday 13.10. 15:00 - 17:00 Seminarraum
  • Tuesday 18.10. 15:00 - 17:00 Seminarraum
  • Thursday 20.10. 15:00 - 17:00 Seminarraum
  • Tuesday 25.10. 15:00 - 17:00 Seminarraum
  • Thursday 27.10. 15:00 - 17:00 Seminarraum
  • Thursday 03.11. 15:00 - 17:00 Seminarraum
  • Tuesday 08.11. 15:00 - 17:00 Seminarraum
  • Thursday 10.11. 15:00 - 17:00 Seminarraum
  • Tuesday 15.11. 15:00 - 17:00 Seminarraum
  • Thursday 17.11. 15:00 - 17:00 Seminarraum
  • Tuesday 22.11. 15:00 - 17:00 Seminarraum
  • Thursday 24.11. 15:00 - 17:00 Seminarraum
  • Tuesday 29.11. 15:00 - 17:00 Seminarraum
  • Thursday 01.12. 15:00 - 17:00 Seminarraum
  • Tuesday 06.12. 15:00 - 17:00 Seminarraum
  • Tuesday 13.12. 15:00 - 17:00 Seminarraum
  • Thursday 15.12. 15:00 - 17:00 Seminarraum
  • Tuesday 10.01. 15:00 - 17:00 Seminarraum
  • Thursday 12.01. 15:00 - 17:00 Seminarraum
  • Tuesday 17.01. 15:00 - 17:00 Seminarraum
  • Thursday 19.01. 15:00 - 17:00 Seminarraum
  • Tuesday 24.01. 15:00 - 17:00 Seminarraum
  • Thursday 26.01. 15:00 - 17:00 Seminarraum
  • Tuesday 31.01. 15:00 - 17:00 Seminarraum

Information

Aims, contents and method of the course

The syllabus is as follows: Arithmetical functions, Dirichlet
product, theory of the unrestricted partion function,
elementary theorems on the distribution of prime numbers,
Dirichlet's Theorem on primes in arithmetic progressions, Dirichlet
characters, Ramanujan sums, Gauss sums, Zetafunctions and L-series,
The Kummer conjecture on Gauss sums, sums of squares and Thetafunctions,
The Waring problems, partition functions and Jacobi product identities.

Assessment and permitted materials

Minimum requirements and assessment criteria

Introduction to the technics and results of analytic number theory.

Examination topics

Reading list

1. Apostol, Tom M.
Introduction to analytic number theory. (English)
Undergraduate Texts in Mathematics. New York-Heidelberg-Berlin:
Springer-Verlag. XII, 338 p. (1976).

2. Brüdern, Jörg
Einführung in die analytische Zahlentheorie. (Introduction to analytic
number theory). (German) Berlin: Springer-Verlag. x, 238 p. (1995).

3. Tenenbaum, Gérald
Introduction to analytic and probabilistic number theory.
Transl. from the 2nd French ed. by C.B.Thomas. (English)
Cambridge Studies in Advanced Mathematics. 46. Cambridge: Cambridge Univ.
Press. xiv, 448 p. (1995).

4. Newman, Donald J.
Analytic number theory. (English)
Graduate Texts in Mathematics. 177. New York, NY: Springer. viii,
76 p. (1998).

5. Chandrasekharan, K.
Introduction to analytic number theory (English)
Berlin-Heidelberg-New York: Springer-Verlag 1968. VIII, 140 p.
with 4 Fig. (1968).

Association in the course directory

Last modified: Mo 07.09.2020 15:40