Maass forms are a particular class of smooth functions defined on a hyperbolic Riemann surface. In the special case of Riemann surfaces associated with a congruence subgroup, it is often the case that results concerning Maass forms bear witness to the existence of profound arithmetic relations. Our main goal is to describe the problem of estimating the triple product functional, explain its significance, and illustrate the representation theoretical techniques employed by Bernstein and Reznikov to make progress. If time permits, we shall discuss non-Archimedean instances of the above theory. I will not be assuming familiarity with any of the abovementioned notions.
This video was produced by Tel Aviv University as part of its algebra seminar.
