2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147021We study the supremum of some random Dirichlet polynomials and obtain sharp upper and lower bounds for supremum expectation that extend the optimal estimate of Halász-Queffélec and enable to cunstruct random polynomials with unusually small maxima. Our approach in proving these results is entirely based on methods of stochastic processes, in particular the metric entropy method.ProbabilityComplex Variables30B50,26D05text