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arXiv · 1810.11340

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

Raf Cluckers·Mircea Mustaţǎ·Kien Huu Nguyen
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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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Raf Cluckers, Mircea Mustaţǎ, Kien Huu Nguyen. 2019-03-19. Igusa's conjecture for exponential sums: optimal estimates for non-rational singularities. https://arxiv.org/abs/1810.11340

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