The Mellin transform of the square of Riemann's zeta-function

Details The Mellin transform of the square of Riemann's zeta-function The Mellin transform of the square of Riemann's zeta-function

2004-11-02

arxiv.org/abs/math/0411040v2

International J. Number Theory 1(2005), 65-73.

Mathematics

Number Theory

9 pages

Scientific paper

Let ${\cal Z}_1(s) = \int_1^\infty |\zeta({1\over2}+ix)|^2x^{-s}{\rm d}x
(\sigma = \Re s > 1)$. A result concerning analytic continuation of ${\cal
Z}_1(s)$ to $\bf C$ is proved, and also a result relating the order of ${\cal
Z}_1(\sigma + it) (1/2 \le \sigma \le 1, t\ge t_0)$ to the order of ${\cal
Z}_1({1\over2}+it)$.

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