Explore the intricate connections between Poincaré series and the linking of Legendrian knots in this 59-minute lecture by G. Rivière from CNRS. Delve into advanced analytic techniques applied to dynamics and geometry, focusing on the fascinating interplay between these mathematical concepts. Gain insights into the application of Poincaré series in the study of Legendrian knots and their linking properties, expanding your understanding of this specialized area of mathematics.