Oscillatory integrals with uniformity in parameters
Eren Mehmet Kiral, Ian Petrow, Matthew P. Young
TL;DR
This paper establishes a precise asymptotic formula for oscillatory integrals with uniform estimates across parameters, enhancing tools for applications in analytic number theory.
Contribution
It provides a sharp asymptotic formula for oscillatory integrals with uniform parameter control, advancing the stationary phase method's applicability.
Findings
Derived a sharp asymptotic formula for specific oscillatory integrals.
Achieved uniform estimates in auxiliary parameters.
Facilitated applications in analytic number theory.
Abstract
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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