The Arithmetic of Power Series and Applications to Irrationality

Explore a groundbreaking mathematical lecture that presents a novel approach to proving the irrationality of certain periods, specifically focusing on the value at 2 of the Dirichlet L-function associated to the primitive quadratic character with conductor -3. Discover how this innovative method leverages rational approximations from existing literature while developing a new theoretical framework to effectively utilize these approximations. Learn about the key component of this approach: an arithmetic holonomy theorem that builds upon foundational work by André, Bost, Charles, and others in arithmetic algebraization theorems through Arakelov theory. Gain insights into collaborative research conducted with Frank Calegari and Vesselin Dimitrov that advances our understanding of the arithmetic properties of power series and their applications to fundamental questions in number theory regarding irrational numbers.