On the Fourth Power Moment of the Riemann Zeta-Function
نویسندگان
چکیده
منابع مشابه
The Twisted Fourth Moment of the Riemann Zeta Function
We compute the asymptotics of the fourth moment of the Riemann zeta function times an arbitrary Dirichlet polynomial of length T 1 11 −ε.
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which is valid for any complex s, it follows that ζ(s) has zeros at s = −2,−4, . . . . These zeros are traditionally called the “trivial” zeros of ζ(s), to distinguish them from the complex zeros of ζ(s), of which the smallest ones (in absolute value) are 12 ± 14.134725 . . . i. It is well-known that all complex zeros of ζ(s) lie in the so-called “critical strip” 0 < σ = Re s < 1, and the Riema...
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The aim of the present article is to exhibit a new proof of the explicit formula for the fourth moment of the Riemann zeta-function that was established by the second named author a decade ago. Our proof is new, particularly in that it dispenses altogether with the spectral theory of sums of Kloosterman sums that played a predominant rôle in the former proof. Our argument is, instead, built dir...
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In 1918 Hardy and Littlewood 2] proved that Z T 1 j(1=2 + it)j 2 dt T log T and in 1926 Ingham 4] showed that Z T 1 j(1=2 + it)j 4 dt 1 2 2 T log 4 T: In general, it is conjectured that if k > 0, then there exists a c k > 0 such that Z T 1 j(1=2 + it)j 2k dt c k T log k 2 T: No value has been suggested for c k if k is diierent from 0,1, or 2. In this paper, we present evidence to support the
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1995
ISSN: 0022-314X
DOI: 10.1006/jnth.1995.1033