Local Suprema of Dirichlet Polynomials and Zerofree Regions of the Riemann Zeta-Function

Details Local Suprema of Dirichlet Polynomials and Zerofree Regions of the Riemann Zeta-Function Local Suprema of Dirichlet Polynomials and Zerofree Regions of the Riemann Zeta-Function

2010-05-21

arxiv.org/abs/1005.3932v2

Mathematics

Number Theory

12

Scientific paper

A new zerofree region of the Riemann Zeta-function $\zeta$ is identified by using Tur\'an's localization criterion linking zeros of $\zeta$ with uniform local suprema of sets of Dirichlet polynomials expanded over the primes. The proof is based on a randomization argument. An estimate for local extrema for some finite families of shifted Dirichlet polynomials, % associated to linearly independent sequences of reals is established by preliminary considering their local increment properties, by means of Montgomery-Vaughan's variant of Hilbert's inequality. A covering argument combined with Tur\'an's localization criterion allows to conclude.

Affiliated with

Also associated with

No associations

Rating

Local Suprema of Dirichlet Polynomials and Zerofree Regions 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 Local Suprema of Dirichlet Polynomials and Zerofree Regions of the Riemann Zeta-Function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local Suprema of Dirichlet Polynomials and Zerofree Regions of the Riemann Zeta-Function will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-339578