Brazilian Journal of Probability and Statistics

[RETRACTED] On Hilbert’s 8th problem

Nicholas G. Polson

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Abstract

The paper is being retracted by the author due to an erratum in the application of Grosswald’s result on the existence of $m_G(s)$, which invalidates the proof of Theorem 2.

Article information

Source
Braz. J. Probab. Stat., Volume 32, Number 3 (2018), 670-678.

Dates
Received: September 2017
Accepted: January 2018
First available in Project Euclid: 8 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1528444877

Digital Object Identifier
doi:10.1214/18-BJPS392

Keywords
RH GGC zeta function

Citation

Polson, Nicholas G. [RETRACTED] On Hilbert’s 8th problem. Braz. J. Probab. Stat. 32 (2018), no. 3, 670--678. doi:10.1214/18-BJPS392. https://projecteuclid.org/euclid.bjps/1528444877


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References

  • Bondesson, L. (1992). Generalised Gamma Convolutions and Related Classes of Distributions and Densities. New York: Springer.
  • Grosswald, E. (1964). Sur la fonction de Riesz. Séminaire Delange-Pisot-Poitou. Théorie des nombres, 6(1), 1–11.
  • Pólya, G. (1926). Bemerkung Über die Integraldarstellung der Riemannschen $\xi$-Funktion. Acta Mathematica 48, 305–317.
  • Riemann, B. (1859). Über die Anzahl der Primzahlen unter einer gegebenen Grösse. Monatsberichte der Berliner Akademie.
  • Roynette, B. and Yor, M. (2005). Infinitely divisible Wald’s couples: Examples linked with the Euler gamma and the Riemann zeta functions. Annales de L’Institut Fourier 55, 1219–1283.
  • Titchmarsh, E. C. (1974). The Theory of the Riemann Zeta-Function. Oxford: Oxford University Press.

See also