On the estimation of $Z_2(s)$

Details On the estimation of $Z_2(s)$ On the estimation of $Z_2(s)$

2003-11-18

arxiv.org/abs/math/0311301v1

in "Anal. Probab. Methods Number Thery" (eds A. Dubickas et al.), TEV, Vilnius 2002, 83-98.

Mathematics

Number Theory

Scientific paper

Estimates for $Z_2(s) = \int_1^|infty |\zeta(1/2+ix)|^4x^{-s}dx (\Re s > 1)$
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 $\int_0^T |\zeta(1/2+it)|^4dt$.

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