Large Spaces Between the Zeros of the Riemann Zeta-Function

Details Large Spaces Between the Zeros of the Riemann Zeta-Function Large Spaces Between the Zeros of the Riemann Zeta-Function

2009-06-30

arxiv.org/abs/0906.5458v3

Mathematics

Number Theory

Scientific paper

In this paper, we will employ the Opial and Wirtinger type inequalities to derive some conditional and unconditional lower bounds for the gaps between the zeros of the Riemann zeta-function. First, we prove (unconditionally) that the consecutive nontrivial zeros often differ by at least 1.9902 times the average spacing. This value improves the value 1.9 due to Mueller and the value 1.9799 due to Montogomery and Odlyzko. Second, on the hypothesis that the 2k-th mixed moments of the Hardy Z-function and its derivative are correctly predicted by random matrix theory, we derive some explicit formulae for the gaps and use them to establish new (conditional) large gaps.

Affiliated with

Also associated with

No associations

Rating

Large Spaces Between the Zeros 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 Large Spaces Between the Zeros of the Riemann Zeta-Function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Large Spaces Between the Zeros of the Riemann Zeta-Function will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-440592