Dear researchers on RG,
Riemann Zeta function and construction of string amplitudes (AdS, flat, even dS spacetime)
Correspondence between RH and scattering properties in quantum field theory (Rachel Berkowitz, 2021):
(https://physics.aps.org/articles/v14/s157)
Note(s) of detailed literature:
Article Amplitudes and the Riemann Zeta Function
Preprint Veneziano Variations: How Unique are String Amplitudes?
Happy New Year !
I believe Virasoro's work and Virasoro-Shapiro was in String Theory. If you are looking for a connection with the Riemann Hypothesis, then you are in beyond the limits of knowledge and you are on your own. However, you might (if you have the time) look into Vinogradov's work applying Fourier Analysis to Number Theory which might be relevant.
The Virasoro-Shapiro amplitude describes certain aspects of the dynamics of relativistic strings. Just like any function it is determined by its singularities. Now it may be the case that these singularities may be related to the zeros of the Riemann zeta function and, in that way, to the Riemann hypothesis (since both are infinite sets); however what must be understood is that these relations are mathematical statements that don't have anything to do with the physical phenomena the Virasoro-Shapiro amplitude is relevant for. Not all infinite sets have the same properties, so it isn't obviously true that studying one can lead to insights about the other. More information is required.
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