2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69239Some results and conjectures on $Z_2(s) = \int_1^\infty |ζ(1/2+ix)|^4x^{-s}dx (\Re s > 1)$ are presented. Consequences of these conjectures regarding the eighth moment of $|ζ(1/2+it)$ and the error term in the fourth moment of $|ζ(1/2+it)$ are discussed.Number Theory11M06; 11F72text