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Matrix Model for Riemann Zeta via its Local Factors

MPS-Authors
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Ghoshal,  Debashis
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1807.07342.pdf
(Preprint), 451KB

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Citation

Chattopadhyay, A., Dutta, P., Dutta, S., & Ghoshal, D. (in preparation). Matrix Model for Riemann Zeta via its Local Factors.


Cite as: http://hdl.handle.net/21.11116/0000-0001-E3DF-4
Abstract
We propose the construction of an ensemble of unitary random matrices (UMM) for the Riemann zeta function. Our approach to this problem is `piecemeal', in the sense that we consider each factor in the Euler product representation of the zeta function to first construct a UMM for each prime $p$. We are able to use its phase space description to write the partition function as the trace of an operator that acts on a subspace of square-integrable functions on the p-adic line. This suggests a Berry-Keating type Hamiltonian. We combine the data from all primes to propose a Hamiltonian and a matrix model for the Riemann zeta function.