Patrick Walls, McMaster University
"The Theta Correspondence and Periods of Automorphic Forms"
The
study
of
periods
of
automorphic
forms
using
the
theta
correspondence
and
the
Weil
representation
was
initiated
by
Waldspurger
about
30
years
ago.
Studying
the
correspondence
for
the
dual
pair
(SL(2),PGL(2))
(or
rather
the
metaplectic
cover
of
SL(2)),
Waldspurger
found
relations
between
Fourier
coefficients,
toric
periods
and
special
values
of
L-functions.
In
this
talk,
we
show
that
there
are
general
relations
among
periods
of
automorphic
forms
for
any
dual
pair
(G,H)
with
applications
to
special
values
of
standard
automorphic
L-functions.