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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2019.1
- 수록면
- 67 - 75 (9page)
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We investigate the averaging value of a random sampling of a Dirichlet series with some condition using Poisson distribution. Our result is the following:Let $L(s)=\sum_{n=1}^{\infty}\frac{a_n}{n^s}$ be a Dirichlet series that converges absolutely for $\mathrm{Re}(s)>1$. If $X_t$ is an increasing random sampling with Poisson distribution and there exists a number $0<\alpha<\frac{1}{2}$ such that $\sum_{n\leq u}a_n\ll u^{\alpha}$, then we have $$\mathbb{E}L(1/2+iX_t) = O(t^{\alpha}\sqrt{\log t}),$$for all sufficiently large $t$ in $ \mathbb{R} $. As a result, we get the behaviour of $L(\frac{1}{2}+it)$ such that $L$ is a Dirichlet $L$-function or a modular $L$-function, when $t$ is sampled by the Poisson distribution.
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참고문헌 (6)
참고문헌 신청
J. L. Hafner / 1989 / On sums of Fourier coefficients of cusp forms / Enseign. Math 35(2):375~382
조시훈 / 2018 / The Averaging Value of a Sampling of the Riemann Zeta Function on the Critical Line Using Poisson Distribution / East Asian Mathematical Journal 34(3):287~293
S. Jo / 2014 / An estimate of the second moment of a sampling of the Riemann zeta function on the critical line / J. Math. Anal. Appl 415:121~134
M. Lifshits / 2009 / Sampling the Lindelof hypothesis with the Cauchy random walk / Proc. Lond. Math. Soc 98(1):241~270
E. Lindelof / 1908 / Quelques remarques sur la croissance de la fonction ζ(s) / Bull. Sci. Math 32:341~356
조시훈 / 2018 / The Averaging Value of a Sampling of the Riemann Zeta Function on the Critical Line Using Poisson Distribution / East Asian Mathematical Journal 34(3):287~293
S. Jo / 2014 / An estimate of the second moment of a sampling of the Riemann zeta function on the critical line / J. Math. Anal. Appl 415:121~134
M. Lifshits / 2009 / Sampling the Lindelof hypothesis with the Cauchy random walk / Proc. Lond. Math. Soc 98(1):241~270
E. Lindelof / 1908 / Quelques remarques sur la croissance de la fonction ζ(s) / Bull. Sci. Math 32:341~356
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