East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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THE AVERAGING VALUE OF A SAMPLING OF THE RIEMANN ZETA FUNCTION ON THE CRITICAL LINE USING POISSON DISTRIBUTION

  • Jo, Sihun (Department of Mathematics Education, Woosuk University)
  • Received : 2018.03.31
  • Accepted : 2018.05.04
  • Published : 2018.05.31
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Abstract

We investigate the averaging value of a random sampling ${\zeta}(1/2+iX_t)$ of the Riemann zeta function on the critical line. Our result is that if $X_t$ is an increasing random sampling with Poisson distribution, then $${\mathbb{E}}{\zeta}(1/2+iX_t)=O({\sqrt{\;log\;t}}$$, for all sufficiently large t in ${\mathbb{R}}$.

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Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

References

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  2. M. Lifshits, M. Weber, Sampling the Lindelof hypothesis with the Cauchy random walk, Proc. Lond. Math. Soc. 98 (2009), no. 1, 241-270. https://doi.org/10.1112/plms/pdn026
  3. E. Lindelof, Quelques remarques sur la croissance de la fonction ${\zeta}$(s), Bull. Sci. Math. 32 (1908), 341-356.
  4. M. Jutila, On the value distribution of the zeta function on the critical line, Bull. London Math. Soc. 15 (1983), no. 5, 513-518. https://doi.org/10.1112/blms/15.5.513

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  1. THE ASYMPTOTIC BEHAVIOUR OF THE AVERAGING VALUE OF SOME DIRICHLET SERIES USING POISSON DISTRIBUTION vol.35, pp.1, 2019, https://doi.org/10.7858/eamj.2019.009