Summary: We apply the Mellin-Barnes integral representation to several situations of interest in mathematical physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions. These results are then employed in different topics in quantum field theory, which include the high-temperature expansion of the free energy of a scalar field in ultrastatic curved spacetime, the asymptotics of the \(p\)-brane density of states, and an explicit approach to the asymptotics of the determinants that appear in string theory.