2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95507We specify sufficient conditions for the square modulus of the local parameters of a family of GL(n) cusp forms to be bounded on average. These conditions are global in nature and are at present satisfied for n less than or equal to 4. As an application, we show that Rankin-Selberg L-functions on GL(m) x GL(n), when m and n are less than or equal to 4, satisfy the standard convexity bound.15 pages; to be published in Archiv der MathematikNumber Theorytext