On some reasons for doubting the Riemann hypothesis
Abstract
Several arguments against the truth of the Riemann hypothesis are extensively discussed. These include the Lehmer phenomenon, the Davenport-Heilbronn zeta-function, large and mean values of |ζ(1/2+it)| on the critical line, and zeros of a class of convolution functions. The first two topics are classical, and the remaining ones are connected with the author's research.
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