Collaborative Number Theory Seminar at the CUNY Graduate CenterCoorganizers: Gautam Chinta, Brooke Feigon, Krzysztof Klosin,
Maria Sabitova,
Lucien Szpiro. Spring 2015 Schedule:
May 15:
Julia Gordon (University of British Columbia) Title: Uniform in p estimates for orbital integrals Abstract:
It is a wellknown theorem of HarishChandra that
the orbital integrals, normalized by the square root
of the discriminant, are bounded (for a fixed test
function). However, it is not easy to see how this
bound behaves if we let the padic field vary (for
example, if the group G is defined over a
number field F, and we consider the family of groups
G_v=G(F_v), as v runs over the set of finite places
of F), and how it varies for a family of test
functions. Using a method based on model theory and
motivic integration, we prove that for a fixed test
function, the bound on orbital integrals can be
taken to be a fixed power (depending on G) of the
cardinality of the residue field, and also obtain a
uniform bound for the family of generators of the
spherical Hecke algebra playing the role of the test
functions. This statement has an application to the
recent work of S.W. Shin and N.Templier on counting
lowlying zeroes of Lfunctions. This project is
joint work with R. Cluckers and I. Halupczok.
