  We discuss a precise relation between the Veneziano amplitude of string
theory, rewritten in terms of ratios of the Riemann zeta function, and two
elementary criteria for the Riemann hypothesis formulated in terms of integrals
of the logarithm and the argument of the zeta function. We also discuss how the
integral criterion based on the argument of the Riemann zeta function relates
to the Li criterion for the Riemann hypothesis. We provide a new generalization
of this integral criterion. Finally, we comment on the physical interpretation
of our recasting of the Riemann hypothesis in terms of the Veneziano amplitude.
