Trigonometric products and Diophantine approximation

12/02/2021, 14:00 - 15:00 in online

Borda, Bence (TU Graz)


Abstract:

The so-called Sudler product is a remarkable trigonometric product related to several areas of mathematics including quantum modular forms, hyperbolic knots and ergodic theory. In this talk we discuss recent asymptotic results based on Diophantine approximation and modularity relations, and highlight a particularly deep connection to quadratic irrationals. Sudler products also exhibit surprisingly delicate random behavior including a central limit theorem. Joint work with Christoph Aistleitner.

Mathematical Sciences Research Centre