Wentang Kuo, Department of Pure Mathematics, University of Waterloo
"On Erd}os-Pomerance conjecture"
Let
k
be
a
global
function
eld
whose
eld
of
constants
is
the
nite
eld
Fq.
Let
1
be
a
xed
place
of
degree
one,
and
A
is
the
ring
of
elements
of
k
which
have
only
1
as
a
pole.
Let
be
a
sgn-normalized
rank
one
Drinfeld
A-module
dened
over
O,
the
integral
closure
of
A
in
the
Hilbert
class
eld
of
A.
We
prove
an
analogue
of
a
conjecture
of
Erd}os
and
Pomerance
for
'.
Given
any
0
6=
2
O
and
an
ideal
M
in
O,
let
f
(M)
=
ff
2
A
j
f
()
0
(mod
M)g
be
the
ideal
in
A.
We
denote
by
!
the
number
of
distinct
prime
ideal
divisors
of
f
(M).
If
q
6=
2,
we
prove
that
there
exists
a
normal
distribution
for
the
quantity!
This
is
the
jointed
work
with
Yen-Liang
Kuan
and
Wei-Chen
Yao.