Abstract
Using the classical analysis resolution of singularities algorithm of [G4], we generalize the theorems of [G3] on Rn sublevel set volumes and oscillatory integrals with real phase function to functions over an arbitrary local field of characteristic zero. The p-adic cases of our results provide new estimates for exponential sums as well as new bounds on how often a function f(x), such as a polynomial with integer coefficients, is divisible by various powers of a prime p when x is an integer. Unlike many papers on such exponential sums and p-adic oscillatory integrals, we do not require the Newton polyhedron of the phase to be nondegenerate, but rather as in [G3] we have conditions on the maximum order of the zeroes of certain polynomials corresponding to the compact faces of this Newton polyhedron.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.