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We study the statistical entropy of a scalar field on the (1+1)-dimensionalMaxwell-dilaton background without an artificial cutoff considering correctionsto all orders in the Planck length from a generalized uncertainty principle(GUP) on the quantum state density. In contrast to the previous results of thehigher dimensional cases having adjustable parameter, we obtain an unadjustableentropy due to the independence of the minimal length while this entropy isproportional to the Bekenstein-Hawking entropy.

Entropy of a (1+1)-dimensional charged black hole to all orders in the Planck length