Xiaomei Zhao, Pure Mathematics Department, University of Waterloo
"New strategies for minor arc estimates: Part I"
We
have
seen
the
outline
of
the
circle
method
in
Waring's
problem
from
Shuntaro's
talks,
where
the
minor
arc
contribution
was
established
by
combining
Weyl's
inequality
with
Hua's
lemma.
In
my
two
talks,
we
will
continue
to
see
some
improvements
on
minor
arc
estimates.
The
first
method
is
to
replace
Hua's
lemma
by
Vinogradov's
mean
value
theorem
(VMVT).
The
second
method
is
Wooley's
recent
strategy
for
transforming
VMVT
to
minor
arc
estimates.
If
time
allows,
we
may
sketch
Ford's
method
as
well.