# Jerusalem Mathematics Colloquium

Thursday, 9th March 2006, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Omer Offen

(Weizmann)

"Spherical functions and some applications in Automorphic Forms"

** Abstract: **
Spherical functions have always played an important role in
harmonic analysis starting with the works of Legendre and Laplace
on spherical harmonics on the sphere in the late 18th century.
In the modern representation theoretic framework they
showed up around 1930 in the work of Cartan and Weyl
on compact symmetric spaces and then around 1950 in the works of
Gelfand, Harish-Chandra and others for non-compact symmetric spaces.

I will review the classical examples of spherical functions and
generalizations thereof,
which are important in the study of automorphic forms.
In the theory of automorphic forms, spherical functions are
one of several ingredients in the local theory.
As an application we will discuss a higher rank analogue of a result of
Waldspurger
that relates a sum of an automorphic form over CM-points to a special
value of an L-function
at the center of symmetry.

This is joint work with E. Lapid.

Light refreshments will be served in the faculty lounge at 3:30.

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