Applications of Wirtinger Inequalities on the Distribution of Zeros of the Riemann Zeta-Function
<p/> <p>On the hypothesis that the <inline-formula> <graphic file="1029-242X-2010-215416-i1.gif"/></inline-formula>th moments of the Hardy <inline-formula> <graphic file="1029-242X-2010-215416-i2.gif"/></inline-formula>-function are...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2010/215416 |
| Summary: | <p/> <p>On the hypothesis that the <inline-formula> <graphic file="1029-242X-2010-215416-i1.gif"/></inline-formula>th moments of the Hardy <inline-formula> <graphic file="1029-242X-2010-215416-i2.gif"/></inline-formula>-function are correctly predicted by random matrix theory and the moments of the derivative of <inline-formula> <graphic file="1029-242X-2010-215416-i3.gif"/></inline-formula> are correctly predicted by the derivative of the characteristic polynomials of unitary matrices, we establish new large spaces between the zeros of the Riemann zeta-function by employing some Wirtinger-type inequalities. In particular, it is obtained that <inline-formula> <graphic file="1029-242X-2010-215416-i4.gif"/></inline-formula> which means that consecutive nontrivial zeros often differ by at least 6.1392 times the average spacing.</p> |
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| ISSN: | 1025-5834 1029-242X |