Transformation properties of Andrews-Beck $NT$ functions and generalized Appell-Lerch series
In 2021, Andrews mentioned that George Beck introduced a partition statistic $NT(r,m,n)$ which is related to Dyson's rank statistic. Motivated by Andrews's work, scholars have established a number of congruences and identities involving $NT(r,m,n)$. In this paper, we strengthen and extend...
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| creator | Chen, Rong Zhu, Xiao-Jie |
| description | In 2021, Andrews mentioned that George Beck introduced a partition statistic
$NT(r,m,n)$ which is related to Dyson's rank statistic. Motivated by Andrews's
work, scholars have established a number of congruences and identities
involving $NT(r,m,n)$. In this paper, we strengthen and extend a recent work of
Mao on the transformation properties of the $NT$ function and provide an
analogy of Hickerson and Mortenson's work on the rank function. As an
application, we demonstrate how one can deduce from our results many identities
involving $NT(r,m,n)$ and another crank-analog statistic $M_\omega(r,m,n)$. As
a related result, some new properties of generalized Appell-Lerch series are
given. |
| doi_str_mv | 10.48550/arxiv.2407.20790 |
| format | Article |
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$NT(r,m,n)$ which is related to Dyson's rank statistic. Motivated by Andrews's
work, scholars have established a number of congruences and identities
involving $NT(r,m,n)$. In this paper, we strengthen and extend a recent work of
Mao on the transformation properties of the $NT$ function and provide an
analogy of Hickerson and Mortenson's work on the rank function. As an
application, we demonstrate how one can deduce from our results many identities
involving $NT(r,m,n)$ and another crank-analog statistic $M_\omega(r,m,n)$. As
a related result, some new properties of generalized Appell-Lerch series are
given.</description><identifier>DOI: 10.48550/arxiv.2407.20790</identifier><language>eng</language><subject>Mathematics - Combinatorics ; Mathematics - Number Theory</subject><creationdate>2024-07</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2407.20790$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2407.20790$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Chen, Rong</creatorcontrib><creatorcontrib>Zhu, Xiao-Jie</creatorcontrib><title>Transformation properties of Andrews-Beck $NT$ functions and generalized Appell-Lerch series</title><description>In 2021, Andrews mentioned that George Beck introduced a partition statistic
$NT(r,m,n)$ which is related to Dyson's rank statistic. Motivated by Andrews's
work, scholars have established a number of congruences and identities
involving $NT(r,m,n)$. In this paper, we strengthen and extend a recent work of
Mao on the transformation properties of the $NT$ function and provide an
analogy of Hickerson and Mortenson's work on the rank function. As an
application, we demonstrate how one can deduce from our results many identities
involving $NT(r,m,n)$ and another crank-analog statistic $M_\omega(r,m,n)$. As
a related result, some new properties of generalized Appell-Lerch series are
given.</description><subject>Mathematics - Combinatorics</subject><subject>Mathematics - Number Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNqFzj0PgjAUheEuDkb9AU7egRWsCEFHNBoH48RoQhq41cbSNrf4-esV4-50ljcnD2PjGY-SRZryqaCHukVxwrMo5tmS99mxIGG8tNSIVlkDjqxDahV6sBJyUxPefbjC6gLBoQhAXk3VhR6EqeGEBklo9cIacudQ63CPVJ3BI30uhqwnhfY4-u2ATbabYr0Lv47SkWoEPcvOU3498__FG1BqQQA</recordid><startdate>20240730</startdate><enddate>20240730</enddate><creator>Chen, Rong</creator><creator>Zhu, Xiao-Jie</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20240730</creationdate><title>Transformation properties of Andrews-Beck $NT$ functions and generalized Appell-Lerch series</title><author>Chen, Rong ; Zhu, Xiao-Jie</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2407_207903</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Combinatorics</topic><topic>Mathematics - Number Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Chen, Rong</creatorcontrib><creatorcontrib>Zhu, Xiao-Jie</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Chen, Rong</au><au>Zhu, Xiao-Jie</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Transformation properties of Andrews-Beck $NT$ functions and generalized Appell-Lerch series</atitle><date>2024-07-30</date><risdate>2024</risdate><abstract>In 2021, Andrews mentioned that George Beck introduced a partition statistic
$NT(r,m,n)$ which is related to Dyson's rank statistic. Motivated by Andrews's
work, scholars have established a number of congruences and identities
involving $NT(r,m,n)$. In this paper, we strengthen and extend a recent work of
Mao on the transformation properties of the $NT$ function and provide an
analogy of Hickerson and Mortenson's work on the rank function. As an
application, we demonstrate how one can deduce from our results many identities
involving $NT(r,m,n)$ and another crank-analog statistic $M_\omega(r,m,n)$. As
a related result, some new properties of generalized Appell-Lerch series are
given.</abstract><doi>10.48550/arxiv.2407.20790</doi><oa>free_for_read</oa></addata></record> |
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| title | Transformation properties of Andrews-Beck $NT$ functions and generalized Appell-Lerch series |
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