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- W3098702479 abstract "Abstract We establish an asymptotic formula describing the horizontal distribution of the zeros of the derivative of the Riemann zeta-function. For ℜ(s) = σ satisfying (log T ) −1/3+ε ⩽ (2σ − 1) ⩽ (log log T ) −2 , we show that the number of zeros of ζ′(s) with imaginary part between zero and T and real part larger than σ is asymptotic to T /(2π(σ−1/2)) as T → ∞. This agrees with a prediction from random matrix theory due to Mezzadri. Hence, for σ in this range the zeros of ζ′(s) are horizontally distributed like the zeros of the derivative of characteristic polynomials of random unitary matrices are radially distributed." @default.
- W3098702479 created "2020-11-23" @default.
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- W3098702479 date "2014-09-29" @default.
- W3098702479 modified "2023-09-23" @default.
- W3098702479 title "On the distribution of the zeros of the derivative of the Riemann zeta-function" @default.
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- W3098702479 doi "https://doi.org/10.1017/s0305004114000413" @default.
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