A note on S(t) and the zeros of the Riemann zeta-function

Let π S(t) denote the argument of the Riemann zeta-function at the point 1/2 + it. Assuming the Riemann hypothesis, we sharpen the constant in the best currently known bounds for S(t) and for the change of S(t) in intervals. We then deduce estimates for the largest multiplicity of a zero of the zeta...

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Veröffentlicht in:The Bulletin of the London Mathematical Society Jg. 39; H. 3; S. 482 - 486
Hauptverfasser: Goldston, D. A., Gonek, S. M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford University Press 01.06.2007
ISSN:0024-6093, 1469-2120
Online-Zugang:Volltext
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Zusammenfassung:Let π S(t) denote the argument of the Riemann zeta-function at the point 1/2 + it. Assuming the Riemann hypothesis, we sharpen the constant in the best currently known bounds for S(t) and for the change of S(t) in intervals. We then deduce estimates for the largest multiplicity of a zero of the zeta-function, and for the largest gap between the zeros.
Bibliographie:ArticleID:bdm032
2000 Mathematics Subject Classification 11M26.
ark:/67375/HXZ-4FD8XJ42-S
istex:B3F619E9F5DAA0F420BCF623D15C2E223871CA47
2000
Mathematics Subject Classification
11M26.
The research of both authors was supported in part by a National Science Foundation FRG grant (DMS 0244660). The first author was also partially supported by NSF grant DMS 0300563, and the second author by NSF grant DMS 0201457. The authors wish to thank the Isaac Newton Institute for its hospitality during their work on this paper, and also the American Institute of Mathematics.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms/bdm032