Geodesic
The Mellin Transform of Hardy's Function is Entire
Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 635-639

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We prove that an appropriately modified Mellin transform of the Hardy function $Z(x)$ is an entire function. The proof is based on the fact that the function $(2^{1-s}-1)\zeta(s)$ is entire.
Keywords: zeta function, Mellin transform, Hardy's function, holomorphic function, entire function, analytic continuation. 
M. Jutila. The Mellin Transform of Hardy's Function is Entire. Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 635-639. http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a14/
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