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- W1497122661 abstract "The Riemann zeta-function $zeta(s)$ is a meromorphic complex-valued function of the complex variable $s$ with the unique pole at $s=1$. It plays a central role in the studies of prime numbers. The upper bound in the critical strip $0le Re(s) le 1$ is an important element in this study. The Lindelof hypothesis conjectured in 1908 asserts that $|zeta(tfrac{1}{2} +it)| =O(tsp{epsilon})$ for sufficiently large $t$. In 1921, Littlewood showed that this is equivalent to an estimate on the number of zeros in certain regions. We use the pseudo-Gamma function recently devised by Cheng and Albeverio in proving the density hypothesis to validate an estimate on the growth rate of zeros and obtain a slightly sharper result than the one which is equivalent with the Lindelof hypothesis. Thus, in particular, we have a proof of the Lindelof hypothesis." @default.
- W1497122661 created "2016-06-24" @default.
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- W1497122661 date "2010-10-16" @default.
- W1497122661 modified "2023-09-27" @default.
- W1497122661 title "Proof of the Linderlof hypothesis" @default.
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