SUBJECT
Title
Special functions
Type of instruction
lecture
Level
master
Faculty
Part of degree program
Credits
3
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
- Gamma function. Stirling formula in the complex plane, saddle point method.
- Zeta function. Functional equation, elementary facts about zeros. Prime number theorem.
- Elliptic functions. Parametrization of elliptic curves, lattices. Fundamental domain for the anharmonic and modular group.
- Functional equation for the theta function. Holomorphic modular forms. Their application to the four square theorem.
Readings
- E.T. Whittaker and G.N. Watson: A Course of Modern Analysis, University Press, Cambridge, 1927.
- E.C. Titchmarsh (and D.R. Heath-Brown: The Theory of the Riemann Zeta-function, Oxford University Press, 1986.
- C.L. Siegel: Topics in Complex Function Theory, John Wiley & Sons, New York, 1988, volume I.
- R.C. Gunning: Lectures on Modular Forms, Princeton University Press, 1962, 96 pages