East Asian mathematical journal

  • 제34권3호
  • /
  • Pages.287-293
  • /
  • 2018
  • /
  • 1226-6973(pISSN)
  • /
  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

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)
  • 투고 : 2018.03.31
  • 심사 : 2018.05.04
  • 발행 : 2018.05.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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 ${\mathbb{R}}$.

키워드

과제정보

연구 과제 주관 기관 : National Research Foundation of Korea (NRF)

참고문헌

  1. S. Jo, M. Yang, An estimate of the second moment of a sampling of the Riemann zeta function on the critical line, J. Math. Anal. Appl. 415 (2014) 121-134. https://doi.org/10.1016/j.jmaa.2014.01.040
  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

피인용 문헌

  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