2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75135In the paper it is discussed the relations of the Riemann $ζ-$function to classes of generating functions of multiply positive sequences according to Schoenberg (also called Pólya frequency sequences). Key words: multiply positive sequences, totally positive sequences, Pólya frequency sequences, Laguerre-Pólya class, Riemann $ζ-$function.22 pagesComplex VariablesNumber Theory30D15, 30D10text