New bounds for exponential sums with a non-degenerate phase polynomial

© 2019 We prove a recent conjecture due to Cluckers and Veys on exponential sums modulo pm for m≥2 in the special case where the phase polynomial f is sufficiently non-degenerate with respect to its Newton polyhedron at the origin. Our main auxiliary result is an improved bound for certain related exponential sums over finite fields. This bound can also be used to settle a conjecture of Denef and Hoornaert on the candidate-leading Taylor coefficient of Igusa's local zeta function associated with a non-degenerate polynomial, at its largest non-trivial real candidate pole.

Publication year:2019

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BOF-publication weight:6

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Authors from:Higher Education

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