On a question of Igusa, II: Uniform asymptotic bounds for Fourier transforms in several variables

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This paper shows that a nontrivial uniform decay estimate for complete exponential sums modulo p r , determined by a polynomial map ${\bf P} = (P_1, P_2)$ follows from the existence of a ‘good P decomposition’ of ${\mathbb Z}_p^n$ , a property that can be proved with geometric methods, and which was introduced in an earlier article by the present author.