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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| Vydáno v: | The Bulletin of the London Mathematical Society Ročník 39; číslo 3; s. 482 - 486 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Oxford University Press
01.06.2007
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| ISSN: | 0024-6093, 1469-2120 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. |
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| Bibliografie: | 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 |