RIEMANN ZETA ZEROS AND PRIME NUMBER SPECTRA IN QUANTUM FIELD THEORY


Autoria(s): Menezes, G.; Svaiter, B. F.; Svaiter, N. F.
Contribuinte(s)

Universidade Estadual Paulista (UNESP)

Data(s)

03/12/2014

03/12/2014

20/10/2013

Resumo

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Riemann hypothesis states that all nontrivial zeros of the zeta function lie in the critical line Re(s) = 1/2. Hilbert and Polya suggested that one possible way to prove the Riemann hypothesis is to interpret the nontrivial zeros in the light of spectral theory. Using the construction of the so-called super-zeta functions or secondary zeta functions built over the Riemann nontrivial zeros and the regularity property of one of this function at the origin, we show that it is possible to extend the Hilbert-Polya conjecture to systems with countably infinite number of degrees of freedom. The sequence of the nontrivial zeros of the Riemann zeta function can be interpreted as the spectrum of a self-adjoint operator of some hypothetical system described by the functional approach to quantum field theory. However, if one considers the same situation with numerical sequences whose asymptotic distributions are not far away from the asymptotic distribution of prime numbers, the associated functional integral cannot be constructed. Finally, we discuss possible relations between the asymptotic behavior of a sequence and the analytic domain of the associated zeta function.

Formato

16

Identificador

http://dx.doi.org/10.1142/S0217751X13501285

International Journal Of Modern Physics A. Singapore: World Scientific Publ Co Pte Ltd, v. 28, n. 26, 16 p., 2013.

0217-751X

http://hdl.handle.net/11449/113061

10.1142/S0217751X13501285

WOS:000326291000005

Idioma(s)

eng

Publicador

World Scientific Publ Co Pte Ltd

Relação

International Journal of Modern Physics A

Direitos

closedAccess

Palavras-Chave #Number theory #zeta regularization #field theory
Tipo

info:eu-repo/semantics/article