2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69146Several 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.30 pagesNumber Theory11M06text