On large gaps between consecutive zeros, on the critical line, of some zeta-functions

Thesis

In this thesis we extend a method of Hall $[30, 34]$ which he used to show the existence of large gaps between consecutive zeros, on the critical line, of the Riemann zeta-function $zeta(s)$. Our modification involves introducing an "amplifier" and enables us to show the existence of gaps between consecutive zeros, on the critical line at height $T,$ of $zeta(s)$ of length at least $2.766 x (2pi/log{T})$. To handle some integral-calculations, we use the article $[44]$ by Hughes and Young....

Expand abstract

Authors: Bredberg, J

• Publication date: 2011
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: Oxford University, UK
• Language: English
• Keywords: Zeta and L-functions; analytic theory
• Subjects: Mathematics; Number theory