Zeros of the Riemann zeta function on the critical line

@article{Feng2010ZerosOT,
  title={Zeros of the Riemann zeta function on the critical line},
  author={S. Feng},
  journal={arXiv: Number Theory},
  year={2010}
}
  • S. Feng
  • Published 2010
  • Mathematics
  • arXiv: Number Theory
it is proved that at least 41.28% zeros of the Riemann zeta function are on the critical line 
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We prove that at least 41.05% of the zeros of the Riemann zeta function are on the critical line.
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Assuming the Riemann Hypothesis, Montgomery and Taylor showed that at least 67.25% of the zeros of the Riemann zeta-function are simple. Using Montgomery and Taylor's argument together with anExpand
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Abstract Explicit lower bounds for the proportion of zeros of the derivatives of Riemann's xi-function which are on the critical line and simple are given. These lead to upper bounds for theExpand
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In this paper we show that at least 2/5 of the zeros of the Riemann zeta-function are simple and on the critical line. Our method is a refinement of the method Levinson [11] used when he showed thatExpand
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The best current bounds for the proportion of zeros of ζ( s ) on the critical line are due to Conrey [C], using Levinson's method [Lev]. This method can also be used to detect simple zeros on theExpand
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Let Asymptotic formulae for I k ( T ) have been established for the cases k =1 (Hardy-Littlewood, see [13]) and k = 2 (Ingham, see [13]). However, the asymptotic behaviour of I k ( T ) remainsExpand
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Publisher Summary This chapter presents an account of Selberg's work on the zeta-function. Selberg's publications concerning the Riemann zeta-function appeared in Norwegian journals at a time whenExpand
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