One-loop effective action and the Riemann zeros

Dueñas, Jesús García de; Svaiter, N. F.; Menezes, G.

doi:10.1142/s0217751x14501826

Cited by 3 publications

(2 citation statements)

References 44 publications

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“…For other approaches discussing the physics of Riemann zeros see [26][27][28][29] . Also, in the literature we can find other recent results connecting number theory and quantum field theory [30][31][32][33][34] .…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of the bosonic randomized Riemann gas

Dueñas¹,

Svaiter²

2015

J. Phys. A: Math. Theor.

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The partition function of a bosonic Riemann gas is given by the Riemann zeta function. We assume that the hamiltonian of this gas at a given temperature β −1 has a random variable ω with a given probability distribution over an ensemble of hamiltonians. We study the average free energy density and average mean energy density of this arithmetic gas in the complex β-plane. Assuming that the ensemble is made by an enumerable infinite set of copies, there is a critical temperature where the average free energy density diverges due to the pole of the Riemann zeta function. Considering an ensemble of non-enumerable set of copies, the average free energy density is non-singular for all temperatures, but acquires complex values in the critical region.Next, we study the mean energy density of the system which depends strongly on the distribution of the non-trivial zeros of the Riemann zeta function. Using a regularization procedure we prove that the this quantity is continuous and bounded for finite temperatures.

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Section: Introductionmentioning

confidence: 99%

Thermodynamics of the bosonic randomized Riemann gas

Dueñas¹,

Svaiter²

2015

J. Phys. A: Math. Theor.

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“…Introducing randomness in the bosonic Riemann gas and studying the thermodynamic variables of this arithmetic gas in the complex β-plane, the connection between the zeros of the Riemann zeta-function and physics was established. For other papers discussing formal aspects of quantum field theory and number theory see the references [21][22][23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Functional equations for regularized zeta-functions and diffusion processes

Saldivar

Svaiter

Zarro

2020

J. Phys. A: Math. Theor.

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We discuss modifications in the integral representation of the Riemann zetafunction that lead to generalizations of the Riemann functional equation that preserves the symmetry s → (1 − s) in the critical strip. By modifying one integral representation of the zeta-function with a cut-off that does exhibit the symmetry x → 1/x, we obtain a generalized functional equation involving Bessel functions of second kind. Next, with another cut-off that does exhibit the same symmetry, we obtain a generalization for the functional equation involving only one Bessel function of second kind. Some connection between one regularized zeta-function and the Laplace transform of the heat kernel for the Euclidean and hyperbolic space is discussed.

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