Stability under scaling in the local phases of multiplicative functions

Autores
Walsh, Miguel Nicolás
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce a strategy to tackle some known obstructions of current approaches to the Fourier uniformity conjecture. Assuming GRH, we then show the conjecture holds for intervals of length at least (log X)^{psi(X)}, with psi(X) -> infty an arbitrarily slowly growing function of X. We expect the methods should adapt to nilsequences, thus also showing that the Generalised Riemann Hypothesis implies close to exponential growth in the sign patterns of the Liouville function.
Fil: Walsh, Miguel Nicolás. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
ABSTRACT HARMONIC ANALYSIS
FOURIER ANALYSIS
MATHEMATICS
NUMBER THEORY
REAL FUNCTIONS
FUNCTIONAL ANALYSIS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/271062
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/271062
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Stability under scaling in the local phases of multiplicative functionsWalsh, Miguel NicolásABSTRACT HARMONIC ANALYSISFOURIER ANALYSISMATHEMATICSNUMBER THEORYREAL FUNCTIONSFUNCTIONAL ANALYSIShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We introduce a strategy to tackle some known obstructions of current approaches to the Fourier uniformity conjecture. Assuming GRH, we then show the conjecture holds for intervals of length at least (log X)^{psi(X)}, with psi(X) -> infty an arbitrarily slowly growing function of X. We expect the methods should adapt to nilsequences, thus also showing that the Generalised Riemann Hypothesis implies close to exponential growth in the sign patterns of the Liouville function.Fil: Walsh, Miguel Nicolás. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaSpringer2025-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/271062Walsh, Miguel Nicolás; Stability under scaling in the local phases of multiplicative functions; Springer; Inventiones Mathematicae; 241; 1; 6-2025; 325-3620020-9910CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00222-025-01343-yinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00222-025-01343-yinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2310.07873info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:16:23Zoai:ri.conicet.gov.ar:11336/271062instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-05 10:16:23.727CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Stability under scaling in the local phases of multiplicative functions
title Stability under scaling in the local phases of multiplicative functions
spellingShingle Stability under scaling in the local phases of multiplicative functions
Walsh, Miguel Nicolás
ABSTRACT HARMONIC ANALYSIS
FOURIER ANALYSIS
MATHEMATICS
NUMBER THEORY
REAL FUNCTIONS
FUNCTIONAL ANALYSIS
title_short Stability under scaling in the local phases of multiplicative functions
title_full Stability under scaling in the local phases of multiplicative functions
title_fullStr Stability under scaling in the local phases of multiplicative functions
title_full_unstemmed Stability under scaling in the local phases of multiplicative functions
title_sort Stability under scaling in the local phases of multiplicative functions
dc.creator.none.fl_str_mv Walsh, Miguel Nicolás
author Walsh, Miguel Nicolás
author_facet Walsh, Miguel Nicolás
author_role author
dc.subject.none.fl_str_mv ABSTRACT HARMONIC ANALYSIS
FOURIER ANALYSIS
MATHEMATICS
NUMBER THEORY
REAL FUNCTIONS
FUNCTIONAL ANALYSIS
topic ABSTRACT HARMONIC ANALYSIS
FOURIER ANALYSIS
MATHEMATICS
NUMBER THEORY
REAL FUNCTIONS
FUNCTIONAL ANALYSIS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We introduce a strategy to tackle some known obstructions of current approaches to the Fourier uniformity conjecture. Assuming GRH, we then show the conjecture holds for intervals of length at least (log X)^{psi(X)}, with psi(X) -> infty an arbitrarily slowly growing function of X. We expect the methods should adapt to nilsequences, thus also showing that the Generalised Riemann Hypothesis implies close to exponential growth in the sign patterns of the Liouville function.
Fil: Walsh, Miguel Nicolás. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We introduce a strategy to tackle some known obstructions of current approaches to the Fourier uniformity conjecture. Assuming GRH, we then show the conjecture holds for intervals of length at least (log X)^{psi(X)}, with psi(X) -> infty an arbitrarily slowly growing function of X. We expect the methods should adapt to nilsequences, thus also showing that the Generalised Riemann Hypothesis implies close to exponential growth in the sign patterns of the Liouville function.
publishDate 2025
dc.date.none.fl_str_mv 2025-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/271062
Walsh, Miguel Nicolás; Stability under scaling in the local phases of multiplicative functions; Springer; Inventiones Mathematicae; 241; 1; 6-2025; 325-362
0020-9910
CONICET Digital
CONICET
url http://hdl.handle.net/11336/271062
identifier_str_mv Walsh, Miguel Nicolás; Stability under scaling in the local phases of multiplicative functions; Springer; Inventiones Mathematicae; 241; 1; 6-2025; 325-362
0020-9910
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00222-025-01343-y
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00222-025-01343-y
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2310.07873
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.084122

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