Oscillatory integrals with uniformity in parameters
Classical Analysis and ODEs
2019-08-28 v2 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.
Cite
@article{arxiv.1710.00916,
title = {Oscillatory integrals with uniformity in parameters},
author = {Eren Mehmet Kiral and Ian Petrow and Matthew P. Young},
journal= {arXiv preprint arXiv:1710.00916},
year = {2019}
}
Comments
Final version. To appear in Journal de Th\'eorie des Nombres de Bordeaux. Portions of this work originally appeared in arXiv:1608.06854 (Petrow-Young) and arXiv:1701.07507 (Kiral-Young). arXiv admin note: text overlap with arXiv:1701.07507