Simple Zeros of the Riemann Zeta-Function |
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Authors: | Conrey JB; Ghosh A; Gonek SM |
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Institution: | Department of Mathematics, Oklahoma State University, College of Arts & Science 401 Mathematical Sciences, Stillwater, OK 74078-0613, USA. E-mail: conrey{at}math.okstate.edu, ghosh{at}math.okstate.edu
Department of Mathematics, University of Rochester Rochester, NY 14627, USA. E-mail: gonek{at}math.rochester.edu |
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Abstract: | Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26. |
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Keywords: | Riemann's zeta-function simple zeros mean value theorems |
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