Mann proved in the 1960s that for any
n
≥
1
n\ge 1
there is a finite set
E
E
of
n
n
-tuples
(
η
1
,
…
,
η
n
)
(\eta _1,\dots , \eta _n)
of complex roots of unity with the following property: if
a
1
,
…
,
a
n
a_1,\dots ,a_n
are any rational numbers and
ζ
1
,
…
,
ζ
n
\zeta _1,\dots ,\zeta _n
are any complex roots of unity such that
∑
i
=
1
n
a
i
ζ
i
=
1
\sum _{i=1}^n a_i\zeta _i=1
and
∑
i
∈
I
a
i
ζ
i
≠
0
\sum _{i\in I} a_i \zeta _i\ne 0
for all nonempty
I
⊆
{
1
,
…
,
n
}
I\subseteq \{1,\dots ,n\}
, then
(
ζ
1
,
…
,
ζ
n
)
∈
E
(\zeta _1,\dots ,\zeta _n)\in E
. Taking an arbitrary field
k
\mathbf {k}
instead of
Q
\mathbb {Q}
and any multiplicative group in an extension field of
k
\mathbf {k}
instead of the group of roots of unity, this property defines what we call a Mann pair
(
k
,
Γ
)
(\mathbf {k}, \Gamma )
. We show that Mann pairs are robust in certain ways, construct various kinds of Mann pairs, and characterize them model-theoretically.