On the mean square of the divisor function in short intervals

Details On the mean square of the divisor function in short intervals On the mean square of the divisor function in short intervals

2007-08-12

arxiv.org/abs/0708.1601v2

J. Th\'eorie des Nombres Bordeaux 21(2009), 195-205

Mathematics

Number Theory

11 pages

Scientific paper

We provide upper bounds for the mean square integral $$ \int_X^{2X}(\Delta_k(x+h) - \Delta_k(x))^2 dx \qquad(h = h(X)\gg1, h = o(x) {\roman{as}} X\to\infty) $$ where $h$ lies in a suitable range. For $k\ge2$ a fixed integer, $\Delta_k(x)$ is the error term in the asymptotic formula for the summatory function of the divisor function $d_k(n)$, generated by $\zeta^k(s)$.

Affiliated with

Also associated with

No associations

Rating

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

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-451081