Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.543059
Title: On large gaps between consecutive zeros, on the critical line, of some zeta-functions
Author: Bredberg, Johan
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2011
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Abstract:
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. Also, we show that Hall's strategy can be applied not only to $zeta(s),$ but also to Dirichlet $L$-functions $L(s,chi),$ where $chi$ is a primitive Dirichlet character. This also enables us to use stronger integral-results, the article $[14]$ by Conrey, Iwaniec and Soundararajan is used. An unconditional result here about large gaps between consecutive zeros, on the critical line, of some Dirichlet $L$-functions $L(s,chi),$ with $chi$ being an even primitive Dirichlet character, is found. However, we will need to use the Generalised Riemann Hypothesis to make sense of the average gap-length between such zeros. Then the gaps, whose existence we show, have a length of at least $3.54$ times the average.
Supervisor: Heath-Brown, Roger Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.543059  DOI: Not available
Keywords: Mathematics ; Number theory ; Zeta and L-functions ; analytic theory
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