On a Formula of Mellin and Its Application to the Study of the Riemann Zeta-function (with an erratum added 03/11/13)

Hisanobu Shinya


In this paper, we reconsider a formula of Mellin. We present a formula which relates the sum of two positive real numbers $m, n$ to their product $mn$. We apply this formula to derivation of a relationship involving the Hurwitz zeta-function. Then we define a series function (stemming from the proved relationship) and discuss an analogy in regard to the Lindel\"{o}f hypothesis. Finally, a proof of the Lindel\"{o}f hypothesis of the Riemann zeta-function is deduced from this analogy.

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DOI: https://doi.org/10.5539/jmr.v4n6p12

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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