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Matti Jutila - An estimate for the Mellin transform of powers of Hardy's function.

hrj:169 - Hardy-Ramanujan Journal, January 1, 2010, Volume 33 - 2010 - https://doi.org/10.46298/hrj.2010.169
An estimate for the Mellin transform of powers of Hardy's function.Article

Authors: Matti Jutila 1,2

  • 1 Departement of Mathematics, University of Turku
  • 2 University of Turku

We show that a certain modified Mellin transform M(s) of Hardy's function is an entire function. There are reasons to connect M(s) with the function ζ(2s1/2), and then the orders of M(s) and ζ(s) should be comparable on the critical line. Indeed, an estimate for M(s) is proved which in the particular case of the critical line coincides with the classical estimate of the zeta-function.


Volume: Volume 33 - 2010
Published on: January 1, 2010
Imported on: March 3, 2015
Keywords: Riemann's zeta-function,Hardy's function,Mellin transform,[MATH]Mathematics [math]

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