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Matematicheskie Zametki, 2010, Volume 88, Issue 4, Pages 635–639
DOI: https://doi.org/10.4213/mzm8856 (Mi mzm8856) 		 
The Mellin Transform of Hardy's Function is Entire

M. Jutila

University of Turku, Finland
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DOI: https://doi.org/10.4213/mzm8856
Abstract: 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.
Received: 02.01.2010
English version:
Mathematical Notes, 2010, Volume 88, Issue 4, Pages 612–616
DOI: https://doi.org/10.1134/S0001434610090348
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: M. Jutila, “The Mellin Transform of Hardy's Function is Entire”, Mat. Zametki, 88:4 (2010), 635–639; Math. Notes, 88:4 (2010), 612–616
Citation in format AMSBIB
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