Rolf Nevanlinna published his groundbreaking study in 1925, based on which a new branch of Function Theory was formed, now known as Nevanlinna theory. Nevanlinna theory, one of the great achievements in mathematical research in the 20th century, forms an important part of the modern function theory. During the last fifteen years, difference versions of Nevanlinna theory have been established, and applied in the theories of complex difference and delay differential equations.
The dissertation of MSc Xinling Liu is concerned with the periodicity of transcendental meromorphic functions, where Nevanlinna theory and its difference versions play important roles. The dissertation contains several new results related to periodicity, such as periodicity with composite functions, uniqueness and complex differential and difference equations. These results aim at a more comprehensive understanding of periodicity of meromorphic functions.
The dissertation also introduces new results on the periodicity of complex differential polynomials, complex difference polynomials and complex differential-difference polynomials. These considerations are inspired by a conjecture due to C.-C. Yang.
The doctoral dissertation of MSc Xinling Liu, entitled The periodicity of transcendental meromorphic functions will be examined at the Faculty of Science and Forestry on the 26th of February 2021 at 12 noon online. The opponent in the public examination will be Assistant Professor Galina Filipuk, University of Warsaw, Poland, and the custos will be Professor Risto Korhonen, University of Eastern Finland. The public examination will be held in English.