Number Theory Seminar

In this talk, we will discuss a new approach to prove irrationality of certain periods; more precisely, we will show that the value at 2 of the Dirichlet L-function associated to the quadratic character with conductor -3 is irrational; we will also show that some products of certain log values are also irrational. Our method uses rational approximations from literature, while we develop a new framework to make use these approximations. The key ingredient is an arithmetic holonomity theorem built upon earlier work by André, Bost, Charles (and others) on arithmetic algebraization theorems via Arakelov theory. This is joint work with Frank Calegari and Vesselin Dimitrov.