On the correlation of shifted values of the Riemann zeta function

Details On the correlation of shifted values of the Riemann zeta function On the correlation of shifted values of the Riemann zeta function

2009-10-05

arxiv.org/abs/0910.0664v1

Mathematics

Number Theory

24 pages

Scientific paper

In 2007, assuming the Riemann Hypothesis (RH), Soundararajan \cite{Moment} proved that $\int_{0}^T |\zeta(1/2 + it)|^{2k} dt \ll_{k, \epsilon} T(\log T)^{k^2 + \epsilon}$ for every $k$ positive real number and every $\epsilon > 0.$ In this paper we generalized his methods to find upper bounds for shifted moments. We also obtained their lower bounds and conjectured asymptotic formulas based on Random matrix model, which is analogous to Keating and Snaith's work. These upper and lower bounds suggest that the correlation of $|\zeta(\h + it + i\alpha_1)|$ and $|\zeta(\h + it + i\alpha_2)|$ transition at $|\alpha_1 - \alpha_2| \approx \frac{1}{\log T}$. In particular these distribution appear independent when $|\alpha_1 - \alpha_2|$ is much larger than $\frac{1}{\log T}.$

Affiliated with

Also associated with

No associations

Rating

On the correlation of shifted values 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 On the correlation of shifted values of the Riemann zeta function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the correlation of shifted values of the Riemann zeta function will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-9249