Oscillatory integrals with uniformity in parameters

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.

Final version. To appear in Journal de Théorie 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

References in corpus (1)

• A generalized cubic moment and the Petersson formula for newforms

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