LF00DE25 Nevanlinna Theory (8 cr)
Cooperation network course
Network: Cross-institutional studies in advanced courses in mathematics and statistics
This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:
- Bachelor's Degree Programme in Mathematics
- Master's Degree Programme in Mathematics
- Bachelor's Degree Programme in Mathematics (Subject Teacher)
- Master's Degree Programme in Mathematics (Subject Teacher)
- Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Doctoral Programme in Mathematics and Statistics
- Doctoral Programme in Mathematics and Science (Specialication in Mathematics)
Description
Nevanlinna’s theory of value distribution is a deep generalization of Picard’s Theorem for meromorphic functions. In this course we will cover the most central contents of Nevanlinna Theory of one complex variable starting from the Poisson-Jensen formula, including the first and the second main theorem of Nevanlinna Theory, the lemma on the logarithmic derivatives, Clunie’s lemma and the defect relations. In addition, some applications of Nevanlinna theory in the theory of differential equations are included in the course.
Learning outcomes
Students master the first and the second main theorems of Nevanlinna Theory, Clunie’s lemma, and the central estimating techniques of logarithmic derivatives. They can apply these results in analyzing value distribution of meromorphic solutions of differential equations.
Additional information
This course is open for everyone.
The course is held every other year during the spring semester.
Description of prerequisites
Basic understanding of complex analysis up to the Cauchy integral formula.