Matrix model for Riemann zeta via its local factors

@article{Chattopadhyay2020MatrixMF,
  title={Matrix model for Riemann zeta via its local factors},
  author={Arghya Chattopadhyay and Parikshit Dutta and Suvankar Dutta and Debashis Ghoshal},
  journal={Nuclear Physics B},
  year={2020}
}

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References

SHOWING 1-10 OF 61 REFERENCES

Phase Space Distribution of Riemann Zeros

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

Random matrix theory and the Riemann zeros II: n -point correlations

Montgomery has conjectured that the non-trivial zeros of the Riemann zeta-function are pairwise distributed like the eigenvalues of matrices in the Gaussian unitary ensemble (GUE) of random matrix

Hamiltonian for the Zeros of the Riemann Zeta Function.

TLDR
A heuristic analysis is presented for the construction of the metric operator to define an inner-product space, on which the Hamiltonian is Hermitian, and it is implied that the Riemann hypothesis holds true.

Random matrix theory and the Riemann zeros. I. Three- and four-point correlations

The non-trivial zeros of the Riemann zeta-function have been conjectured to be pairwise distributed like the eigenvalues of matrices in the Gaussian Unitary Ensemble (GUE) of random matrix theory.

Complements to Li's Criterion for the Riemann Hypothesis☆

Abstract In a recent paper Xian-Jin Li showed that the Riemann Hypothesis holds if and only ifλn=∑ρ [1−(1−1/ρ)n] hasλn>0 forn=1, 2, 3, … whereρruns over the complex zeros of the Riemann zeta

Trace formula in noncommutative geometry and the zeros of the Riemann zeta function

Abstract. We give a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while eventual noncritical zeros appear as resonances. We give a geometric

On adelic model of boson Fock space

We construct a canonical embedding of the Schwartz space on $R^n$ to the space of distributions on the adelic product of all the $p$-adic numbers. This map is equivariant with respect to the action

Comment on "Hamiltonian for the Zeros of the Riemann Zeta Function"

This comment about the article "Hamiltonian for the Zeros of the Riemann Zeta Function", by C. M. Bender, D. C. Brody, and M. P. M\"uller, published recently in Phys. Rev. Lett. (Phys. Rev. Lett.,

The Riemann Zeros and Eigenvalue Asymptotics

TLDR
It is speculated that the Riemann dynamics is related to the trajectories generated by the classical hamiltonian Hcl=XP, and very refined features of the statistics of the tn can be computed accurately from formulae with quantum analogues.
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