On Tuesday, November 6, 2018, Pierre VILLEMOT, PhD student at the Laboratory of Mathematics (LAMA), will defend his thesis "Lemmas of zeros and distribution of values of meromorphic functions".
The defense will be held at 2 p.m., in Building 21, on the Bourget-du-Lac campus.
Summary of the thesis
This thesis deals with the arithmetic properties of meromorphic and transcendent functions of a variable. In Chapter 3, we define measures of transcendence for holomorphic and meromorphic functions on a regular domain of C and then increase these measures according to the distribution of small values of the function under study. Using the theories of Nevanlinna and Ahlfors, we study in Chapter 4 the distribution of small values of certain classes of meromorphic functions on D or C in order to obtain explicit increases in their transcendence measurements. The main application of this work is to obtain new lemmas of zero polynomials for large families of meromorphic functions and in particular for Weierstrass functions and Fuchsian functions. In Chapter 5, we show that these lemmas of polynomial zeros lead to logarithmic bounds of the number of algebraic points of degree and bounded height contained in the graphs of the functions studied.