Oscillatory integrals with uniformity in parameters

By E. M. Kıral, Ian Petrow, M. Young. Journal de Théorie des Nombres de Bordeaux, 2017

51 citations recorded by the source corpus.

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 applications in analytic number theory.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/4c1001e7163594daabe2a8a8ea9a39e104d7b53a

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In Algebra and Number Theory

1. Ian Petrow
2. M. Young
3. Siegfred Baluyot
4. Stephan Baier
5. Manjul Bhargava
6. A. Shankar
7. Alexandra Florea

In Applied Mathematics

1. Ian Petrow
2. M. Young
3. A. Shankar
4. Manjul Bhargava
5. Siegfred Baluyot

Citations in the corpus

• A generalized cubic moment and the Petersson formula for newforms (2016, background): “≥ 1 and all tin the support of w. Let I= Z∞ −∞ w(t)eiφ(t)dt. If |φ′(t)| ≫ Y Z for all tin the support of w, then I≪AZR−A for Aarbitrarily large. 10.3. Stationary phase. Nowwe quote themaintheorem from[KPY]which extends [BKY, Proposition 8.2]. Theorem 10.3 ([KPY]). Suppose wT is X-inert in t1,...td, ”
• The Weyl bound for Dirichlet L-functions of cube-free conductor (2018, background): “l to (2.16) except that g+(x) is replaced by g−(x) defined by (2.17) g−(x) = 4 π Z ∞ 0 K2it(x)sinh(πt)th(t)dt. 3. Conventions and terminology for weight functions We begin with a useful definition from [KPY]. Let F be an index set and X= XT : F → R≥1 be a function of T∈ F. Definition 3.1. A family {wT}”