  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 of 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.
