We present (some) connections and implications of superstring amplitudes
from and to number theory. These relations include motivic multiple zeta
values, single-valued multiple zeta values, Drinfeld, and Deligne associators. More concretely, we will show that
tree-level superstring amplitudes provide a
beautiful link between generalized multiple Gaussian hypergeometric functions and the decomposition of motivic
multiple zeta values.
Furthermore, we establish relations between complex integrals on CP^1 minus 3 points as single-valued projection of
iterated real integrals on RP^1 minus 3 points.
From the the physical point of view this relation expresses closed string amplitudes as projections of open string
amplitudes: a relation, which goes far beyond, what is known from the notorious Kawai-Lewellen-Tye (KLT) relations.