On the moments of the Riemann zeta-function in short intervals

Details On the moments of the Riemann zeta-function in short intervals On the moments of the Riemann zeta-function in short intervals

2008-07-08

arxiv.org/abs/0807.1181v2

See Hardy-Ramanujan J. 32(2009), 4-23, www.nias.res.in/hrj/contentsvol32.htm

Mathematics

Number Theory

10 pages

Scientific paper

Assuming the Riemann Hypothesis it is proved that, for fixed $k>0$ and $H = T^\theta$ with fixed $0<\theta \le 1$, $$ \int_T^{T+H}|\zeta(1/2+it)|^{2k} dt \ll H(\log T)^{k^2(1+O(1/\log_3T))}, $$ where $\log_jT = \log(\log_{j-1}T)$. The proof is based on the recent method of K. Soundararajan for counting the occurrence of large values of $\log|\zeta(1/2+it)|$, who proved that $$ \int_0^{T}|\zeta(1/2+it)|^{2k} dt \ll_\epsilon T(\log T)^{k^2+\epsilon}. $$

Affiliated with

Also associated with

No associations

Rating

On the moments of the Riemann zeta-function in short intervals 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 On the moments of the Riemann zeta-function in short intervals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the moments of the Riemann zeta-function in short intervals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-268328