2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129767A short proof of the generalized Riemann hypothesis (gRH in short) for zeta functions $ζ_{k}$ of algebraic number fields $k$ - based on the Hecke's proof of the functional equation for $ζ_{k}$ and the method of the proof of the Riemann hypothesis derived in [$M_{A}$] (algebraic proof of the Riemann hypothesis) is given. The generalized Riemann hypothesis for Dirichlet L-functions is an immediately consequence of (gRH) for $ζ_{k}$ and suitable product formula which connects the Dedekind zetas with L-functions.47 pagesGeneral Mathematics11M26text