Phase Space Distribution of Riemann Zeros

Abstract

We present the partition function of a most generic $U(N)$ single plaquette model in terms of representations of unitary group. Extremising the partition function in large N limit we obtain a relation between eigenvalues of unitary matrices and number of boxes in the most dominant Young tableaux distribution. Since, eigenvalues of unitary matrices behave like coordinates of free fermions whereas, number of boxes in a row is like conjugate momenta of the same, a relation between them allows us to provide a phase space distribution for different phases of the unitary model under consideration. This proves a universal feature that all the phases of a generic unitary matrix model can be described in terms of topology of free fermi phase space distribution. Finally, using this result and analytic properties of resolvent that satisfy Dyson-Schwinger equation, we present a phase space distribution of unfolded zeros of Riemann zeta function.

40 pages, 5 figures

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Cited by in corpus (4)

• Emergent Phase Space Description of Unitary Matrix Model
• From Phase Space to Integrable Representations and Level-Rank Duality
• $U(N)$ Torus Link Invariants in the Large $N$ limit from Matrix Model Approach
• A Unitary Matrix Model for $q$-deformed Plancherel Growth