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Simple Proofs of Some Bernstein–Mordell Type Inequalities Read chapter Read first chapter

2014 | OriginalPaper | Chapter

On a Hybrid Fourth Moment Involving the Riemann Zeta-Function

Authors : Aleksandar Ivić, Wenguang Zhai

Published in: Topics in Mathematical Analysis and Applications

Publisher: Springer International Publishing

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Abstract

For each integer 1 ≤ j ≤ 6, we provide explicit ranges for σ for which the asymptotic formula
$$\displaystyle{\int _{0}^{T}\left \vert \zeta \left (\frac{1} {2} + it\right )\right \vert ^{4}\vert \zeta (\sigma +it)\vert ^{2j}dt \sim T\sum _{ k=0}^{4}a_{ k,j}(\sigma )\log ^{k}T}$$
holds as T → ∞, where ζ(s) is the Riemann zeta-function. The obtained ranges improve on an earlier result of the authors. An application to a weighted divisor problem is also given.

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previous chapter Hypergeometric Representation of Certain Summation–Integral Operators
next chapter On the Invertibility of Some Elliptic Operators on Manifolds with Boundary and Cylindrical Ends
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Metadata
Title
On a Hybrid Fourth Moment Involving the Riemann Zeta-Function
Authors
Aleksandar Ivić
Wenguang Zhai
Copyright Year
2014
Book
Topics in Mathematical Analysis and Applications

Print ISBN: 978-3-319-06553-3

Electronic ISBN: 978-3-319-06554-0

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-06554-0_19

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