On Tuesday, November 6, 2018, Pierre VILLEMOT, a doctoral student at the Mathematics Laboratory (LAMA), will defend his dissertation titled “Zero lemmas and the distribution of values of meromorphic functions.”
The defense will take place at 2:00 p.m. in Building 21 on the Bourget-du-Lac campus.
Thesis summary
This thesis focuses on the arithmetic properties of meromorphic and transcendental functions of one variable. In Chapter 3, we define measures of transcendence for holomorphic and meromorphic functions on a regular domain of ℝ, and then we bound these measures based on the distribution of the small values of the function under study. Using the theories of Nevanlinna and Ahlfors, in Chapter 4 we study the distribution of small values of certain classes of meromorphic functions on D or C in order to obtain explicit bounds on their transcendence measures. The main application of this work is the derivation of new polynomial zero lemmas for large families of meromorphic functions, and in particular for Weierstrass functions and Fuchsian functions. In Chapter 5, we show that these polynomial zero lemmas lead to logarithmic bounds on the number of algebraic points of bounded degree and height contained in the graphs of the functions studied.