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Additive averages of multiplicative correlation sequences and applications
We study sets of recurrence, in both measurable and topological settings, for actions of (ℕ, ×) and (ℚ >0 , ×). In particular, we show that autocorrelation sequences of positive functions arising from multiplicative systems have positive additive averages. We also give criteria for when sets of t...
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| Published in: | Journal d'analyse mathématique (Jerusalem) 2023-04, Vol.149 (2), p.719-761 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c268t-f8d6d08d15558f16e30c4f6388ea2367c3aa49c2f3311addcf691ef7b11684c33 |
| container_end_page | 761 |
| container_issue | 2 |
| container_start_page | 719 |
| container_title | Journal d'analyse mathématique (Jerusalem) |
| container_volume | 149 |
| creator | Donoso, Sebastián Le, Anh N. Moreira, Joel Sun, Wenbo |
| description | We study sets of recurrence, in both measurable and topological settings, for actions of (ℕ, ×) and (ℚ
>0
, ×). In particular, we show that autocorrelation sequences of positive functions arising from multiplicative systems have positive additive averages. We also give criteria for when sets of the form {(
an
+
b
)
1
/(
cn
+
d
)
ℓ
:
n
∈ ℕ} are sets of multiplicative recurrence, and consequently we recover two recent results in number theory regarding completely multiplicative functions and the Omega function. |
| doi_str_mv | 10.1007/s11854-022-0264-x |
| format | article |
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>0
, ×). In particular, we show that autocorrelation sequences of positive functions arising from multiplicative systems have positive additive averages. We also give criteria for when sets of the form {(
an
+
b
)
1
/(
cn
+
d
)
ℓ
:
n
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>0
, ×). In particular, we show that autocorrelation sequences of positive functions arising from multiplicative systems have positive additive averages. We also give criteria for when sets of the form {(
an
+
b
)
1
/(
cn
+
d
)
ℓ
:
n
∈ ℕ} are sets of multiplicative recurrence, and consequently we recover two recent results in number theory regarding completely multiplicative functions and the Omega function.</description><subject>Abstract Harmonic Analysis</subject><subject>Analysis</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Functional Analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number theory</subject><subject>Partial Differential Equations</subject><issn>0021-7670</issn><issn>1565-8538</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kE9LAzEQxYMoWKsfwNuC52gm2WSzx1LUKgUveg4xf8qW7WZNdkv99qZuwZOHYQbm994MD6FbIPdASPWQACQvMaE0lyjx4QzNgAuOJWfyHM0IoYArUZFLdJXSlhDOa0Zn6HVhbTM0e1fovYt641IRfLEb26Hp28bo35UJMbo2z6ErkvsaXWcypztb6P5EhS5dowuv2-RuTn2OPp4e35crvH57flku1thQIQfspRWWSAucc-lBOEZM6QWT0mnKRGWY1mVtqGcMQFtrvKjB-eoTQMjSMDZHd5NvH0P-JQ1qG8bY5ZOKSqiFIJUUmYKJMjGkFJ1XfWx2On4rIOoYmZoiUzkydYxMHbKGTpqU2W7j4p_z_6IfTg1v6w</recordid><startdate>20230401</startdate><enddate>20230401</enddate><creator>Donoso, Sebastián</creator><creator>Le, Anh N.</creator><creator>Moreira, Joel</creator><creator>Sun, Wenbo</creator><general>The Hebrew University Magnes Press</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20230401</creationdate><title>Additive averages of multiplicative correlation sequences and applications</title><author>Donoso, Sebastián ; Le, Anh N. ; Moreira, Joel ; Sun, Wenbo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-f8d6d08d15558f16e30c4f6388ea2367c3aa49c2f3311addcf691ef7b11684c33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Analysis</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Functional Analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number theory</topic><topic>Partial Differential Equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Donoso, Sebastián</creatorcontrib><creatorcontrib>Le, Anh N.</creatorcontrib><creatorcontrib>Moreira, Joel</creatorcontrib><creatorcontrib>Sun, Wenbo</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal d'analyse mathématique (Jerusalem)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Donoso, Sebastián</au><au>Le, Anh N.</au><au>Moreira, Joel</au><au>Sun, Wenbo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Additive averages of multiplicative correlation sequences and applications</atitle><jtitle>Journal d'analyse mathématique (Jerusalem)</jtitle><stitle>JAMA</stitle><date>2023-04-01</date><risdate>2023</risdate><volume>149</volume><issue>2</issue><spage>719</spage><epage>761</epage><pages>719-761</pages><issn>0021-7670</issn><eissn>1565-8538</eissn><abstract>We study sets of recurrence, in both measurable and topological settings, for actions of (ℕ, ×) and (ℚ
>0
, ×). In particular, we show that autocorrelation sequences of positive functions arising from multiplicative systems have positive additive averages. We also give criteria for when sets of the form {(
an
+
b
)
1
/(
cn
+
d
)
ℓ
:
n
∈ ℕ} are sets of multiplicative recurrence, and consequently we recover two recent results in number theory regarding completely multiplicative functions and the Omega function.</abstract><cop>Jerusalem</cop><pub>The Hebrew University Magnes Press</pub><doi>10.1007/s11854-022-0264-x</doi><tpages>43</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-7670 |
| ispartof | Journal d'analyse mathématique (Jerusalem), 2023-04, Vol.149 (2), p.719-761 |
| issn | 0021-7670 1565-8538 |
| language | eng |
| recordid | cdi_proquest_journals_2819660786 |
| source | Springer Nature |
| subjects | Abstract Harmonic Analysis Analysis Dynamical Systems and Ergodic Theory Functional Analysis Mathematics Mathematics and Statistics Number theory Partial Differential Equations |
| title | Additive averages of multiplicative correlation sequences and applications |
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