Effective estimation of some oscillatory integrals related to infinitely divisible distributions

Sandro Bettin (1) , Sary Drappeau (2)

1 UniGe - Università degli studi di Genova = University of Genoa
2 I2M - Institut de Mathématiques de Marseille

We present a practical framework to prove, in a simple way, two-terms asymptotic expansions for Fourier integrals $$ {\mathcal I}(t) = \int_{\mathbb R}({\rm e}^{it\phi(x)}-1) {\rm d} \mu(x) $$ where $\mu$ is a probability measure on $\mathbb{R}$ and $\phi$ is measurable. This applies to many basic cases, in link with Levy's continuity theorem. We present applications to limit laws related to rational continued fractions coefficients.

Domaines: Théorie des nombres [math.NT]

Sandro Bettin, Sary Drappeau. Effective estimation of some oscillatory integrals related to infinitely divisible distributions. 2020. ⟨hal-02998544v1⟩