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Published September 28, 2011 | Submitted
Journal Article Open

The 4.36th Moment of the Riemann Zeta-Function


Conditionally on the Riemann Hypothesis, we obtain bounds of the correct order of magnitude for the 2kth moment of the Riemann zeta-function for all positive real k<2.181. This provides for the first time an upper bound of the correct order of magnitude for some k>2; the case of k=2 corresponds to a classical result of Ingham [11]. We prove our result by establishing a connection between moments with k>2 and the so-called twisted fourth moment. This allows us to appeal to a recent result of Hughes and Young [10]. Furthermore we obtain a point-wise bound for |ζ(1/2 + it)|^(2r) (with 0

Additional Information

© The Author(s) 2011. Published by Oxford University Press. Received July 28, 2011; Accepted August 8, 2011. Advance Access Publication September 28, 2011. This work was partially supported by an NSERC PGS-D award.

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