If
L
(
a
,
s
)
:=
∑
n
c
(
n
,
a
)
n
−
s
L(a,s):=\sum _n c(n,a)n^{-s}
is a family of “geometric”
L
−
L-
functions depending on a parameter
a
a
, then the function
(
p
,
a
)
↦
c
(
p
,
a
)
(p,a)\mapsto c(p,a)
, where
p
p
runs through the set of prime integers, is not a rational function and hence is not a function belonging to algebraic geometry. The aim of the paper is to show that if one enlarges algebraic geometry by “adjoining a Fermat quotient operation”, then the functions
c
(
p
,
a
)
c(p,a)
become functions in the enlarged geometry at least for
L
−
L-
functions of curves and Abelian varieties.