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Quantum Field Theory is plagued by divergences in the attempt to calculatephysical quantities. Standard techniques of regularization and renormalizationare used to keep under control such a problem. In this paper we would like touse a different scheme based on Modified Dispersion Relations (MDR) to removeinfinities appearing in one loop approximation in contrast to what happens inconventional approaches. In particular, we apply the MDR regularization to thecomputation of the entropy of a Schwarzschild black hole from one side and theZero Point Energy (ZPE) of the graviton from the other side. The graviton ZPEis connected to the cosmological constant by means of of the Wheeler-DeWittequation.

Modified Dispersion Relations: from Black-Hole Entropy to the Cosmological Constant