English

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.

Keywords

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

R2 v1 2026-06-22T22:01:44.179Z