The 4.36-th moment of the Riemann zeta-function

Details The 4.36-th moment of the Riemann zeta-function The 4.36-th moment of the Riemann zeta-function

2011-06-23

arxiv.org/abs/1106.4806v2

Mathematics

Number Theory

10 pages; Fixed errors in Section 3. Proof of Thm 2 (now Corollary 1) shorter; Added a few comments following Proposition 1

Scientific paper

Conditionally on the Riemann Hypothesis we obtain bounds of the correct order of magnitude for the 2k-th 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. 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. Furthermore we obtain a point-wise bound for |zeta(1/2 + it)|^{2r} (with 0 < r < 1) that can be regarded as a multiplicative analogue of Selberg's bound for S(T). We also establish asymptotic formulae for moments (k < 2.181) slightly off the half-line.

Affiliated with

Also associated with

No associations

Rating

The 4.36-th moment of the Riemann zeta-function does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The 4.36-th moment of the Riemann zeta-function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The 4.36-th moment of the Riemann zeta-function will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-470548