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.Comment: 30 page