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. 
@article{MZM_2010_88_4_a14,
     author = {M. Jutila},
     title = {The {Mellin} {Transform} of {Hardy's} {Function} is {Entire}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {635--639},
     publisher = {mathdoc},
     volume = {88},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a14/}
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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/