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On a question of Igusa, II: Uniform asymptotic bounds for Fourier transforms in several variables
Published online by Cambridge University Press: 01 December 2004
Abstract
This paper shows that a nontrivial uniform decay estimate for complete exponential sums modulo pr, 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.
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- Foundation Compositio Mathematica 2005
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