Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang–Xie–Zhang

Let [Formula: see text] denote the overpartition function. In this paper, our primary goal is to study the asymptotic behavior of the finite differences of the logarithm of the overpartition function, i.e., [Formula: see text] , by studying the inequality of the following form [Formula: see text] wh...

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Autor principal: Mukherjee, Gargi
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9763134/
https://www.ncbi.nlm.nih.gov/pubmed/36573919
http://dx.doi.org/10.1007/s40993-022-00420-y
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author Mukherjee, Gargi
author_facet Mukherjee, Gargi
author_sort Mukherjee, Gargi
collection PubMed
description Let [Formula: see text] denote the overpartition function. In this paper, our primary goal is to study the asymptotic behavior of the finite differences of the logarithm of the overpartition function, i.e., [Formula: see text] , by studying the inequality of the following form [Formula: see text] where [Formula: see text] are computable constants depending on the positive integer r, determined explicitly. This solves a problem posed by Wang, Xie and Zhang in the context of searching for a better lower bound of [Formula: see text] than 0. By settling the problem, we are able to show that [Formula: see text]
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spelling pubmed-97631342022-12-21 Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang–Xie–Zhang Mukherjee, Gargi Res Number Theory Research Let [Formula: see text] denote the overpartition function. In this paper, our primary goal is to study the asymptotic behavior of the finite differences of the logarithm of the overpartition function, i.e., [Formula: see text] , by studying the inequality of the following form [Formula: see text] where [Formula: see text] are computable constants depending on the positive integer r, determined explicitly. This solves a problem posed by Wang, Xie and Zhang in the context of searching for a better lower bound of [Formula: see text] than 0. By settling the problem, we are able to show that [Formula: see text] Springer International Publishing 2022-12-19 2023 /pmc/articles/PMC9763134/ /pubmed/36573919 http://dx.doi.org/10.1007/s40993-022-00420-y Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Research
Mukherjee, Gargi
Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang–Xie–Zhang
title Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang–Xie–Zhang
title_full Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang–Xie–Zhang
title_fullStr Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang–Xie–Zhang
title_full_unstemmed Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang–Xie–Zhang
title_short Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang–Xie–Zhang
title_sort inequalities for higher order differences of the logarithm of the overpartition function and a problem of wang–xie–zhang
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9763134/
https://www.ncbi.nlm.nih.gov/pubmed/36573919
http://dx.doi.org/10.1007/s40993-022-00420-y
work_keys_str_mv AT mukherjeegargi inequalitiesforhigherorderdifferencesofthelogarithmoftheoverpartitionfunctionandaproblemofwangxiezhang

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