On Applications of Spherical Functions on Spherical Varieties and Integral Representations of L-functions
This is the last talk of a series of four talks on the discussion of the papers [Sak08], [Sak13] and [Sak12]. The present talk consists of two parts. In the first part of this talk I will first briefly review some results in the previous talks and then discuss [Sak13, Part 3] on applications of the explicit formulae for spherical functions on spherical varieties. In the second part of this talk I will give an overview of the paper [Sak12] with emphasis on section 3 and section 4 which I hope it can be served as an introduction to that paper.
References
[Sak08] Yiannis Sakellaridis. On the unramified spectrum of spherical varieties over p-adic fields. Compositio Mathematica, 144(4):978–1016, 2008.
[Sak12] Yiannis Sakellaridis. Spherical varieties and integral representations of L-functions . Algebra number theory, 6(4):611–667, 2012.
[Sak13] Yiannis Sakellaridis. Spherical functions on spherical varieties. American Journal of Mathematics, 135(5):1291–1381, 2013.
