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On the estimation of $Z_2(s)$

Aleksandar Ivić
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Abstract

Estimates for $Z_2(s) = \int_1^|infty |ζ(1/2+ix)|^4x^{-s}dx (\Re s > 1)$ are discussed, both pointwise and in mean square. It is shown how these estimates can be used to bound $E_2(T)$, the error term in the asymptotic formula for $\int_0^T |ζ(1/2+it)|^4dt$.

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Aleksandar Ivić. 2003-11-18. On the estimation of $Z_2(s)$. https://arxiv.org/abs/math/0311301

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