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A note on S(t) and the zeros of the Riemann zeta-function |
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| Authors: | Goldston D A; Gonek S M |
| Institution: | Department of Mathematics San Jose State University San Jose, CA 95192 USA goldston{at}math.sjsu.edu Department of Mathematics University of Rochester Rochester, NY 14627 USA gonek{at}math.rochester.edu |
| Abstract: | Let  S(t) denote the argument of the Riemann zeta-function atthe point 1/2 + it. Assuming the Riemann hypothesis, we sharpenthe constant in the best currently known bounds for S(t) andfor the change of S(t) in intervals. We then deduce estimatesfor the largest multiplicity of a zero of the zeta-function,and for the largest gap between the zeros. |
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