Unicité des Fonctions Entières & Equations Différentielles Linéaires - Rabab BOUABDELLI (My University, 2015)
This thesis is on the topic of Nevanlinna theory, a powerful tool from complex analysis. In this thesis, we begin by studying how Nevanlinna Theory is derived, and continue by showing how its results and methods can be used to solve some interesting problems like unicity problem of entire functions, and differential equations. We end by visiting the p-adic universe. Such a visit offers a glimpse of a part of mathematics which is both important and fun, and which also is something of a meeting point between algebra and complex analysis.
Keywords: Complex analysis, Nevanlinna theory, order, exponent of convergence, oscillation, differential equation, iterated order, [p; q]-order, unicity of entire function, Brück Conjecture, q-difference, q-wronskian, p-adic