Asymptotic density of open p-brane states with zero-modes included

We obtain the asymptotic density of open p-brane states with zero-modes included. The resulting logarithmic correction to the p-brane entropy has a coefficient −p+22p, and is independent of the dimension of the embedding spacetime. Such logarithmic corrections to the entropy, with precisely this coefficient, appear in two other contexts also: a gas of massless particles in p-dimensional space, and a Schwarzschild black hole in (p+2)-dimensional anti-de Sitter spacetime.