Universität Wien

250033 VO Analytic number theory (2010S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 04.03. 15:00 - 17:00 Seminarraum
  • Monday 08.03. 15:00 - 17:00 Seminarraum
  • Thursday 11.03. 15:00 - 17:00 Seminarraum
  • Monday 15.03. 15:00 - 17:00 Seminarraum
  • Thursday 18.03. 15:00 - 17:00 Seminarraum
  • Monday 22.03. 15:00 - 17:00 Seminarraum
  • Thursday 25.03. 15:00 - 17:00 Seminarraum
  • Monday 12.04. 15:00 - 17:00 Seminarraum
  • Thursday 15.04. 15:00 - 17:00 Seminarraum
  • Monday 19.04. 15:00 - 17:00 Seminarraum
  • Thursday 22.04. 15:00 - 17:00 Seminarraum
  • Monday 26.04. 15:00 - 17:00 Seminarraum
  • Thursday 29.04. 15:00 - 17:00 Seminarraum
  • Monday 03.05. 15:00 - 17:00 Seminarraum
  • Thursday 06.05. 15:00 - 17:00 Seminarraum
  • Monday 10.05. 15:00 - 17:00 Seminarraum
  • Monday 17.05. 15:00 - 17:00 Seminarraum
  • Thursday 20.05. 15:00 - 17:00 Seminarraum
  • Thursday 27.05. 15:00 - 17:00 Seminarraum
  • Monday 31.05. 15:00 - 17:00 Seminarraum
  • Monday 07.06. 15:00 - 17:00 Seminarraum
  • Thursday 10.06. 15:00 - 17:00 Seminarraum
  • Monday 14.06. 15:00 - 17:00 Seminarraum
  • Thursday 17.06. 15:00 - 17:00 Seminarraum
  • Monday 21.06. 15:00 - 17:00 Seminarraum
  • Thursday 24.06. 15:00 - 17:00 Seminarraum
  • Monday 28.06. 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

Written exam or oral exam after the end of the lecture.

Minimum requirements and assessment criteria

familiarity with advanced results and methods of number theory

Examination topics

varying

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

MALV

Last modified: Mo 07.09.2020 15:40