Entry requirements

Mathematics, 60 ECTS credits including Complex

analysis MN1, Fourier Analysis MN1.

Aims

To give a deeper knowledge on selected parts

of

complex analysis in one variable and to point out applications of

complex analysis e.g. to number theory.

Content

Infinite series and products. Partial fraction

developments and factorisation of analytic functions.

Analytic continuation. Gamma- and beta-functions, Stirling's

formula,

method of steepest descent, zeta-functions and prime numbers

(Riemann

hypothesis), distribution of zeros of analytic

functions,

normal families, proof of the Riemann mapping

theorem. Harmonic functions.

Poisson's summation

formula, Jensen's formula. Subharmonic functions.

Dirichlet's problem.

Instruction

Lectures and problem solving sessions.

Assessment

Written and oral examination at the end of the

course. Compulsory hand-in assignments during

the course. Compulsory project work whenever

such a project occurs in the course.