Aims

The main objective is the study of the main theorems concerning complex analytic functions of one complex variable

Main themes

The lectures will focus on the study of analytic functions in the complex plane, and on their singularities. After some preliminaries on the Cauchy theorems and on the residue theorem, we study the meromorphic functions on the complex projective space and on the complex tori (elliptic functions). Geometric considerations and classification of 1 dimensional representations of tori will lead to various results on elliptic functions and to algebraic geometry. The course will end with a study of the space of modules of complex tori and the construction of modular functions.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Prerequisites: analyse (candidature level).

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