Relations among the Riemann Zeta and Hurwitz Zeta Functions, as Well as Their Products
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In this paper, several relations are obtained among the Riemann zeta and Hurwitz zeta functions, as well as their products. A particular case of these relations give rise to a simple re-derivation of the important results of Katsurada and Matsumoto on the mean square of the Hurwitz zeta function. Also, a relation derived here provides the starting point of a novel approach which, in a series of companion papers, yields a formal proof of the Lindelöf hypothesis. Some of the above relations motivate the need for analysing the large α behaviour of the modified Hurwitz zeta function ζ 1 ( s , α ) , s ∈ C , α ∈ ( 0 , ∞ ) , which is also presented here.
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2005 ◽
Vol 117
(3)
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pp. 373-381
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1994 ◽
Vol 38
(1)
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pp. 71-78
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2009 ◽
Vol 85
(99)
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pp. 1-17
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