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We discuss a precise relation between the Veneziano amplitude of stringtheory, rewritten in terms of ratios of the Riemann zeta function, and twoelementary criteria for the Riemann hypothesis formulated in terms of integralsof the logarithm and the argument of the zeta function. We also discuss how theintegral criterion based on the argument of the Riemann zeta function relatesto the Li criterion for the Riemann hypothesis. We provide a new generalizationof this integral criterion. Finally, we comment on the physical interpretationof our recasting of the Riemann hypothesis in terms of the Veneziano amplitude.

From Veneziano to Riemann: A String Theory Statement of the Riemann Hypothesis