2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67446If $(k,\ell)$ is an exponent pair such that $k+\ell<1$, then we have $$ \int_1^T|ζ(1/2+it)|^4|ζ(σ+it)|^2dt \ll_εT^{1+ε}\quad(σ> \min({5\over6},\max(\ell-k, {5k+\ell\over4k+1})), $$ while if $(k,\ell)$ is an exponent pair such that $3k+\ell<1$, then we have $$ \int_1^T|ζ(1/2+it)|^4|ζ(σ+it)|^4dt \ll_εT^{1+ε}\quad(σ> {11k+\ell+1\over8k+2}). $$9 pages, only TeX formatting correctedNumber Theory11M06text