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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

Ben Lichtin
Ben Lichtin
Affiliation:
49 Boardman Street, Rochester, NY 14607, USAlichtin@math.rochester.edu
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Abstract

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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.

Keywords

fiber integralsingular seriespolynomial mappingexponential sums11L0311L0714B0514G2032S45
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 1 , January 2005 , pp. 192 - 226
Copyright
Foundation Compositio Mathematica 2005