Abstract
Extending previous work on the thermodynamics of quantum strings a low-temperature power series expansion is derived with the help of the Meinardus theorem for the free energy of a quantum p-brane having toroidal compactification. In the string case p = 1 this series has a finite radius of convergence corresponding to the well-known Hagedorn temperature. For p>1 the radius of convergence drops to zero. However, for odd p it is possible to resum unambiguously the divergent power series in temperature T to a form in which T is unrestricted. This suggests that odd p-branes at least there may be no limiting temperature, and moreover there may exist a fundamental difference between even and odd p-branes.
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