## 3 Citations

### A $$p$$-arton model for modular cusp forms

- MathematicsTheoretical and Mathematical Physics
- 2021

We propose to associate to a modular form (an infinite number of) complex valued functions on the p-adic numbers Qp for each prime p. We elaborate on the correspondence and study its consequences in…

### Phase operator on $L^2(\mathbb{Q}_p)$ and the zeroes of Fisher and Riemann

- Mathematics
- 2021

The distribution of the non-trivial zeroes of the Riemann zeta function, according to the Riemann hypothesis, is tantalisingly similar to the zeroes of the partition functions (Fisher and Yang-Lee…

### Pseudodifferential Operators on $${\mathbb{Q}_p}$$ and $$L$$-Series

- Mathematicsp-Adic Numbers, Ultrametric Analysis and Applications
- 2021

We define a family of pseudodifferential operators on the Hilbert space $L^2(\mathbf{Q}_p)$ of complex valued square-integrable functions on the $p$-adic number field $\mathbf{Q}_p$. The Riemann…

## References

SHOWING 1-10 OF 61 REFERENCES

### Phase Space Distribution of Riemann Zeros

- Mathematics
- 2016

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

- Mathematics
- 1996

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.

- MathematicsPhysical review letters
- 2017

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

- Mathematics
- 1995

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☆

- Mathematics
- 1999

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

- Mathematics
- 1997

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

- Mathematics
- 2006

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"

- Philosophy
- 2017

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

- MathematicsSIAM Rev.
- 1999

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.