Entropy of the Schwarzschild black hole to all orders in the Planck length

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Considering corrections to all orders in the Planck length on the quantum state density from a generalized uncertainty principle (GUP), we calculate the statistical entropy of the scalar field on the background of the Schwarzschild black hole without any cutoff. We obtain the entropy of the massive scalar field proportional to the horizon area.
13 pages, 1 figure; Minor typos corrected, one reference added; Accepted for publication in Phys. Lett. B

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