Let
m
≥
2
m\geq 2
be a natural number and let
A
\mathcal {A}
be an ideal class of an imaginary quadratic number field. Zagier and Gangl constructed
C
/
Q
(
m
)
\mathbb {C}/\mathbb {Q}(m)
-valued invariants
I
m
(
A
)
I_{m}(\mathcal {A})
which they named “the enhanced zeta value”, since the real part of
i
m
−
1
I
m
(
A
)
i^{m-1}I_{m}(\mathcal {A})
, after being multiplied by a certain elementary factor in terms of a factorial and a power of
2
π
2\pi
, equals the partial zeta value
ζ
(
m
,
A
)
\zeta (m,\mathcal {A})
. They also constructed the enhanced polylogarithm, a
C
/
Q
(
m
)
\mathbb {C}/\mathbb {Q}(m)
-valued function on the
m
m
-th Bloch group
B
m
(
C
)
\mathcal {B}_{m}(\mathbb {C})
, and formulated an enhanced conjecture for
I
m
(
A
)
I_{m}(\mathcal {A})
that gives a natural lift of the polylogarithm conjecture for
ζ
(
m
,
A
)
\zeta (m,\mathcal {A})
to a conjectural equality in
C
/
Q
(
m
)
\mathbb {C}/\mathbb {Q}(m)
. In this article, we define the Shintani L-function of two variables which is naturally regarded as a two-variable analog of the partial zeta function for imaginary quadratic fields. Then we study its analytic properties in order to construct
C
/
Q
(
1
)
\mathbb {C}/\mathbb {Q}(1)
-valued invariants
Λ
i
(
1
−
m
,
A
)
\Lambda _{i}(1-m,\mathcal {A})
(
i
∈
{
1
,
2
}
i\in \{1,2\}
) for a ray class
A
\mathcal {A}
using the first partial derivative of the Shintani L-function at
(
1
−
m
,
1
−
m
)
(1-m,1-m)
. From the construction,
Λ
1
(
1
−
m
,
A
)
\Lambda _{1}(1-m,\mathcal {A})
and
Λ
2
(
1
−
m
,
A
)
\Lambda _{2}(1-m,\mathcal {A})
are complex conjugate invariants that satisfy
ζ
′
(
1
−
m
,
A
)
=
Λ
1
(
1
−
m
,
A
)
+
Λ
2
(
1
−
m
,
A
)
\zeta ’(1-m,\mathcal {A})=\Lambda _{1}(1-m,\mathcal {A})+\Lambda _{2}(1-m,\mathcal {A})
. Then we prove the main theorem of this article about the equality between Zagier and Gangl’s enhanced zeta value
I
m
(
A
)
I_{m}(\mathcal {A})
and
Λ
1
(
1
−
m
,
A
)
\Lambda _{1}(1-m,\mathcal {A})
, by explicit calculation of the Fourier expansion of the partial derivative of the Shintani L-function. Finally, we formulate the enhanced conjecture for the ray class invariants
Λ
i
(
1
−
m
,
A
)
\Lambda _{i}(1-m,\mathcal {A})
, by which we expand Zagier-Gangl’s original conjecture. We also give several numerical examples to verify the correctness of our enhanced conjecture.