Van der Corput and metric theorems for geometric progressions for self-similar measures

Amir Algom; Yuanyang Chang; Meng Wu; Yu Liang Wu

doi:10.1007/s00208-025-03233-3

Van der Corput and metric theorems for geometric progressions for self-similar measures

Amir Algom, Yuanyang Chang, Meng Wu, Yu Liang Wu

Department of Mathematics, Physics and Computer Science (Oranim Campus)

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a van der Corput lemma for non-atomic self-similar measures. As an application, we show that the correlations of all finite orders of converge to the Poissonian model for -a.e. x, assuming. We also complete a recent result of Algom, Rodriguez Hertz, and Wang (obtained simultaneously by Baker and Banaji), showing that any self-conformal measure with respect to a non-affine real analytic IFS has polynomial Fourier decay.

Original language	English
Pages (from-to)	183-214
Number of pages	32
Journal	Mathematische Annalen
Volume	393
Issue number	1
DOIs	https://doi.org/10.1007/s00208-025-03233-3
State	Published - Sep 2025

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00208-025-03233-3

Cite this

@article{fbed91486ff24816abdd4158d4ffb40e,

title = "Van der Corput and metric theorems for geometric progressions for self-similar measures",

abstract = "We prove a van der Corput lemma for non-atomic self-similar measures. As an application, we show that the correlations of all finite orders of converge to the Poissonian model for -a.e. x, assuming. We also complete a recent result of Algom, Rodriguez Hertz, and Wang (obtained simultaneously by Baker and Banaji), showing that any self-conformal measure with respect to a non-affine real analytic IFS has polynomial Fourier decay.",

author = "Amir Algom and Yuanyang Chang and Meng Wu and Wu, \{Yu Liang\}",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2025.",

year = "2025",

month = sep,

doi = "10.1007/s00208-025-03233-3",

language = "English",

volume = "393",

pages = "183--214",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Van der Corput and metric theorems for geometric progressions for self-similar measures

AU - Algom, Amir

AU - Chang, Yuanyang

AU - Wu, Meng

AU - Wu, Yu Liang

PY - 2025/9

Y1 - 2025/9

N2 - We prove a van der Corput lemma for non-atomic self-similar measures. As an application, we show that the correlations of all finite orders of converge to the Poissonian model for -a.e. x, assuming. We also complete a recent result of Algom, Rodriguez Hertz, and Wang (obtained simultaneously by Baker and Banaji), showing that any self-conformal measure with respect to a non-affine real analytic IFS has polynomial Fourier decay.

AB - We prove a van der Corput lemma for non-atomic self-similar measures. As an application, we show that the correlations of all finite orders of converge to the Poissonian model for -a.e. x, assuming. We also complete a recent result of Algom, Rodriguez Hertz, and Wang (obtained simultaneously by Baker and Banaji), showing that any self-conformal measure with respect to a non-affine real analytic IFS has polynomial Fourier decay.

UR - https://www.scopus.com/pages/publications/105012753931

U2 - 10.1007/s00208-025-03233-3

DO - 10.1007/s00208-025-03233-3

M3 - Article

AN - SCOPUS:105012753931

SN - 0025-5831

VL - 393

SP - 183

EP - 214

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 1

ER -

Van der Corput and metric theorems for geometric progressions for self-similar measures

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this