Igusa's conjecture for exponential sums: optimal estimates for non-rational singularities
Number Theory
2019-03-20 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1810.11340,
title = {Igusa's conjecture for exponential sums: optimal estimates for non-rational singularities},
author = {Raf Cluckers and Mircea Mustaţǎ and Kien Huu Nguyen},
journal= {arXiv preprint arXiv:1810.11340},
year = {2019}
}