2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157987We introduce a "resonance" method to produce large values of $|ζ(1/2+it)|$ and large and small central values of $L$-functions.16 pages; Version 2 makes a few light revisions. To appear in Math. AnnalenNumber TheoryClassical Analysis and ODEstext