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

Saskia Chambille; Kien Huu Nguyen

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arXiv · 1709.02682

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

Saskia Chambille·Kien Huu Nguyen

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Abstract

In this paper, we will give two proofs of the Cluckers-Veys conjecture on exponential sums for the case of polynomials in $\mathbb{Z}[x_{1},\ldots,x_{n}]$ 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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Saskia Chambille, Kien Huu Nguyen. 2017-09-08. Proof of Cluckers-Veys's conjecture on exponential sums for polynomials with log-canonical threshold at most a half. https://arxiv.org/abs/1709.02682

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