  The interplay of unitarity and analyticity has long been known to impose
strong constraints on scattering amplitudes in quantum field theory and string
theory. This has been highlighted in recent times in a number of papers and
lecture notes. Here we examine such conditions in the context of superstring
tree-level scattering amplitudes, leading to positivity constraints on
determinants of Hankel matrices involving polynomials of multiple zeta values.
These generalise certain constraints on polynomials of single zeta values in
the mathematics literature.
