The Distribution of Rational Points on Some Spherical Varieties.
28 SEP 2021
18:30 - 21:00
In this talk I will discuss a work in progress in which, together with Sho Tanimoto and Yuri Tschinkel, we study the distribution of rational points on some anisotropic spherical varieties of rank 1 over an arbitrary number field. Our work is the non-split analogue of the results of Valentin Blomer, Jorg Brudern, Ulrich Derenthal, and Giuliano Gagliardi where they consider split spherical varieties of rank 1 over the rational numbers, though our methods are completely different. In our proof we use the theory of automorphic forms, especially Waldspurger's celebrated theorem on toric periods, to analyse the height zeta function. Once this analysis is done, the result on the distribution of rational points follows from a standard Tauberian theorem. We hope to address split spherical varieties of rank 1 over an arbitrary number field using similar methods in a future work.
Meeting ID: 908 611 6889