Proof of Cluckers-Veys's conjecture on exponential sums for polynomials with log-canonical threshold at most a half

2017/09/08 by Saskia Chambille, Chambille, Saskia, Kien Huu Nguyen +1
Mathematics · #03C98 11L05 11S40 11U09 12L12 14E18 #11L07 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:03C98 #msc:11L05 #msc:11L07 #msc:11S40 #msc:11U09 #msc:12L12 #msc:14E18

paper · pdf · doi:10.48550/arxiv.1709.02682

arxiv created 2017/09/08 · arxiv updated 2017/09/11

Abstract

In this paper, we will give two proofs of the Cluckers-Veys conjecture on exponential sums for the case of polynomials in ℤ[x₁,…,x_n] having log-canonical thresholds at most one half. In particular, these results imply Igusa's conjecture and Denef-Sperber's conjecture under the same restriction on the log-canonical threshold.

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