Exponential sums on Aⁿ, III

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We give two applications of our earlier work "Exponential sums on Aⁿ, II" (math.AG/9909009). We compute the p-adic cohomology of certain exponential sums on Aⁿ involving a polynomial whose homogeneous component of highest degree defines a projective hypersurface with at worst weighted homogeneous isolated singularities. This study was motivated by recent work of Garcia (Exponential sums and singular hypersurfaces, Manuscripta Math., v. 97 (1998), pp. 45-58). We also compute the p-adic cohomology of certain exponential sums on Aⁿ whose degree is divisible by the characteristic.