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From Veneziano to Riemann: A string theory statement of the Riemann hypothesis

He, Y., Jejjala, V. and Minic, D. (2016). From Veneziano to Riemann: A string theory statement of the Riemann hypothesis. International Journal of Modern Physics A, 31(36), 1650201.. doi: 10.1142/S0217751X16502018

Abstract

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.

Publication Type: Article
Additional Information: Electronic version of an article published as: Int. J. Mod. Phys. A 31, 1650201 (2016) [31 pages] http://dx.doi.org/10.1142/S0217751X16502018 © World Scientific Publishing Company http://www.worldscientific.com/worldscinet/ijmpa
Publisher Keywords: Riemann zeta function; Hilbert–Pólya programme; string amplitude
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/16802
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