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

TL;DR

This paper proves the Cluckers-Veys conjecture on exponential sums for polynomials with low log-canonical thresholds, confirming related conjectures like Igusa's and Denef-Sperber's under the same conditions.

Contribution

It provides two proofs of the conjecture for polynomials with log-canonical thresholds at most one half, advancing understanding of exponential sums in this context.

Findings

Proofs confirm the conjecture for the specified class of polynomials.

Results imply Igusa's and Denef-Sperber's conjectures under the same conditions.

Enhances theoretical understanding of exponential sums and log-canonical thresholds.

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.