#### Conference abstracts

Session B3 - Symbolic Analysis - Semi-plenary talk

July 14, 17:00 ~ 17:50

## The linear Mahler equation: linear and algebraic relations

A Mahler function is a solution, analytic in some neighborhood of the origin, of a linear difference equation associated with the Mahler operator $z\mapsto z^q$, where $q\geq 2$ is an integer. Understanding the nature of such functions at algebraic points of the complex open unit disc is an old number theoretical problem dating back to the pioneering works of Mahler in the late 1920s. In this talk, I will explain why it can be considered as totally solved now, after works of Ku. Nishioka, Philippon, Faverjon and the speaker.