Simple error bounds for an asymptotic expansion of the partition function
Recently, there has been renewed interest in studying the asymptotic properties of the integer partition function p ( n ). Hardy, Ramanujan, and Rademacher provided detailed asymptotic analysis for p ( n ). Presently, attention has shifted towards Poincaré-type asymptotic expansions, characterised b...
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| Veröffentlicht in: | The Ramanujan journal 2024-12, Vol.65 (4), p.1757-1771 |
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| container_title | The Ramanujan journal |
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| creator | Nemes, Gergő |
| description | Recently, there has been renewed interest in studying the asymptotic properties of the integer partition function
p
(
n
). Hardy, Ramanujan, and Rademacher provided detailed asymptotic analysis for
p
(
n
). Presently, attention has shifted towards Poincaré-type asymptotic expansions, characterised by their simplicity albeit reduced accuracy compared to the earlier works of Hardy, Ramanujan, and Rademacher. This paper aims to establish computable error bounds for one such simplified expansion. The bounds presented herein are sharper, and their derivation is considerably simpler compared to those found in recent literature. |
| doi_str_mv | 10.1007/s11139-024-00958-8 |
| format | Article |
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p
(
n
). Hardy, Ramanujan, and Rademacher provided detailed asymptotic analysis for
p
(
n
). Presently, attention has shifted towards Poincaré-type asymptotic expansions, characterised by their simplicity albeit reduced accuracy compared to the earlier works of Hardy, Ramanujan, and Rademacher. This paper aims to establish computable error bounds for one such simplified expansion. The bounds presented herein are sharper, and their derivation is considerably simpler compared to those found in recent literature.</description><identifier>ISSN: 1382-4090</identifier><identifier>EISSN: 1572-9303</identifier><identifier>DOI: 10.1007/s11139-024-00958-8</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Asymptotic properties ; Asymptotic series ; Combinatorics ; Error analysis ; Field Theory and Polynomials ; Fourier Analysis ; Functions of a Complex Variable ; Mathematics ; Mathematics and Statistics ; Number Theory ; Partitions (mathematics)</subject><ispartof>The Ramanujan journal, 2024-12, Vol.65 (4), p.1757-1771</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-308f0bbb10032d090e4f7fc023b2ac398eef6eee3a472713b2ccc9fb4c4b17003</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11139-024-00958-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11139-024-00958-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Nemes, Gergő</creatorcontrib><title>Simple error bounds for an asymptotic expansion of the partition function</title><title>The Ramanujan journal</title><addtitle>Ramanujan J</addtitle><description>Recently, there has been renewed interest in studying the asymptotic properties of the integer partition function
p
(
n
). Hardy, Ramanujan, and Rademacher provided detailed asymptotic analysis for
p
(
n
). Presently, attention has shifted towards Poincaré-type asymptotic expansions, characterised by their simplicity albeit reduced accuracy compared to the earlier works of Hardy, Ramanujan, and Rademacher. This paper aims to establish computable error bounds for one such simplified expansion. The bounds presented herein are sharper, and their derivation is considerably simpler compared to those found in recent literature.</description><subject>Asymptotic properties</subject><subject>Asymptotic series</subject><subject>Combinatorics</subject><subject>Error analysis</subject><subject>Field Theory and Polynomials</subject><subject>Fourier Analysis</subject><subject>Functions of a Complex Variable</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number Theory</subject><subject>Partitions (mathematics)</subject><issn>1382-4090</issn><issn>1572-9303</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9UE1LAzEUDKJgrf4BTwHP0ZePNrtHKX4UBA_qOSRpolvaZE2yYP-9WVfw5ukNw8y8YRC6pHBNAeRNppTylgATBKBdNKQ5QjO6kIy0HPhxxbxhREALp-gs5y0ACOByhtYv3b7fOexSigmbOIRNxr5CHbDOh31fYuksdl-9DrmLAUePy4fDvU6lKyPhh2BHcI5OvN5ld_F75-jt_u519Uienh_Wq9snYhlAIRwaD8aYWpuzTS3khJfeAuOGacvbxjm_dM5xLSSTtLLW2tYbYYWhsprm6GrK7VP8HFwuahuHFOpLxSmTwJdMNlXFJpVNMefkvOpTt9fpoCiocTI1TabqZOpnMjWa-GTKVRzeXfqL_sf1DSUIbzc</recordid><startdate>20241201</startdate><enddate>20241201</enddate><creator>Nemes, Gergő</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20241201</creationdate><title>Simple error bounds for an asymptotic expansion of the partition function</title><author>Nemes, Gergő</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-308f0bbb10032d090e4f7fc023b2ac398eef6eee3a472713b2ccc9fb4c4b17003</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Asymptotic properties</topic><topic>Asymptotic series</topic><topic>Combinatorics</topic><topic>Error analysis</topic><topic>Field Theory and Polynomials</topic><topic>Fourier Analysis</topic><topic>Functions of a Complex Variable</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number Theory</topic><topic>Partitions (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nemes, Gergő</creatorcontrib><collection>CrossRef</collection><jtitle>The Ramanujan journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nemes, Gergő</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Simple error bounds for an asymptotic expansion of the partition function</atitle><jtitle>The Ramanujan journal</jtitle><stitle>Ramanujan J</stitle><date>2024-12-01</date><risdate>2024</risdate><volume>65</volume><issue>4</issue><spage>1757</spage><epage>1771</epage><pages>1757-1771</pages><issn>1382-4090</issn><eissn>1572-9303</eissn><abstract>Recently, there has been renewed interest in studying the asymptotic properties of the integer partition function
p
(
n
). Hardy, Ramanujan, and Rademacher provided detailed asymptotic analysis for
p
(
n
). Presently, attention has shifted towards Poincaré-type asymptotic expansions, characterised by their simplicity albeit reduced accuracy compared to the earlier works of Hardy, Ramanujan, and Rademacher. This paper aims to establish computable error bounds for one such simplified expansion. The bounds presented herein are sharper, and their derivation is considerably simpler compared to those found in recent literature.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11139-024-00958-8</doi><tpages>15</tpages></addata></record> |
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| issn | 1382-4090 1572-9303 |
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| subjects | Asymptotic properties Asymptotic series Combinatorics Error analysis Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics Number Theory Partitions (mathematics) |
| title | Simple error bounds for an asymptotic expansion of the partition function |
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