Mellin transform of superstring amplitude reduces to Riemann zeta function in forward limit and supplies a new closed-form expression for its EFT expansion at finite t.
Nonclassical Degrees of Freedom in the Riemann Hamiltonian
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abstract
The Hilbert-Polya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum hamiltonian. If so, conjectures by Katz and Sarnak put this hamiltonian in Altland and Zirnbauer's universality class C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros.
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Zeta Functions and the Superstring
Mellin transform of superstring amplitude reduces to Riemann zeta function in forward limit and supplies a new closed-form expression for its EFT expansion at finite t.