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Oscillatory integrals with uniformity in parameters

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arxiv 1710.00916 v2 pith:XIOJPXN5 submitted 2017-10-02 math.CA math.NT

Eren Mehmet Kiral , Ian Petrow , Matthew P. Young This is my paper · ORCID
classification math.CAmath.NT
keywords integralsoscillatoryparametersanalyticapplicationapproachedasymptoticauxiliary
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We prove a sharp asymptotic formula for certain oscillatory integrals that may be approached using the stationary phase method. The estimates are uniform in terms of auxiliary parameters, which is crucial for application in analytic number theory.

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  1. Squarefree numbers in short intervals: explicit and formalized

    math.NT 2026-08 conditional novelty 6.0 of 10

    For intervals of length H = X^{1/5 - 2/90935 + ε}, the number of squarefree integers differs from (6/π²)H by at most an explicit constant times H X^{-ε/10^{25}}.

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