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- W1994495199 abstract "The paper describes a computational estimation of the constant $beta (1)$ characterizing the bounds of $left vert zeta (1+it)right vert$. It is known that as $trightarrow infty$ begin{equation*} frac {zeta (2)}{2beta (1)e^{gamma }left [ 1+o(1)right ] log log t}leq left vert zeta (1+it)right vert leq 2beta (1)e^{gamma }left [ 1+o(1) right ] log log t end{equation*} with $beta (1)geq frac {1}{2}$, while the truth of the Riemann hypothesis would also imply that $beta (1)leq 1$. In the range $1<tleq 10^{16}$, two sets of estimates of $beta (1)$ are computed, one for increasingly small minima and another for increasingly large maxima of $left vert zeta (1+it)right vert$. As $t$ increases, the estimates in the first set rapidly fall below $1$ and gradually reach values slightly below $0.70$, while the estimates in the second set rapidly exceed $frac {1}{2}$ and gradually reach values slightly above $0.64$. The obtained numerical results are discussed and compared to the implications of recent theoretical work of Granville and Soundararajan." @default.
- W1994495199 created "2016-06-24" @default.
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- W1994495199 date "2008-09-01" @default.
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- W1994495199 title "Computational estimation of the constant $beta (1)$ characterizing the order of $zeta (1+it)$" @default.
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- W1994495199 doi "https://doi.org/10.1090/s0025-5718-08-02065-6" @default.
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