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On the Fourth Power Moment of the Riemann Zeta-Function

✍ Scribed by A. Ivic; Y. Motohashi

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 770 KB
Volume: 51
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1995.1033

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✦ Synopsis

The function (E_{2}(R)) is used to denote the error term in the asymptotic formula for the fourth power moment of the Riemann zeta-function on the half-line. In this paper we prove several new results concerning this function, which include (O) - and (\Omega)-results. In the proofs use is made of the second author's explicit formula for a weighted integral involving the fourth moment on the half-line, and his results on spectral mean values of Maass wave form (L)-functions. ' 1995 Academic Press. Inc.

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## Abstract In this paper, we have exhibited, by utilizing value distribution theory, some new properties of the Gamma function Γ(__z__) and the Riemann zeta function ζ(__z__). Specifically, we have proved that both of the two functions are prime and the Riemann zeta function, like Γ(__z__), does n