Igusa's conjecture for exponential sums: optimal estimates for non-rational singularities

2018/10/26 by Raf Cluckers, Mircea Mustaţă, Cluckers, Raf +4 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Meromorphic and Entire Functions #math.AG #math.NT #msc:11L05 #msc:11L07 #msc:11S40 #msc:14E30

paper · pdf · doi:10.48550/arxiv.1810.11340

arxiv created 2019/03/19 · arxiv updated 2019/03/20

Abstract

We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa's conjecture on exponential sums, with the log-canonical threshold in the exponent of the estimates. We show that this covers optimally all situations of the conjectures for non-rational singularities, by comparing the log canonical threshold with a local notion of the motivic oscillation index.

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• On The Local Sum Conjecture in Two Dimensions

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