Definition
(Zeta function)
.
The zeta function
Z
C
(
T
)
of a smooth projective curve
C
∕
𝔽
q
is defined by
Z
C
(
T
)
=
exp
(
∑
n
=
1
∞
#
C
(
𝔽
q
n
)
n
T
n
)
.