Evaluation of Hecke–Rogers series and expansions of the rank function
A formula is established for the evaluation of double series of Hecke–Rogers type in terms of theta functions and Appell–Lerch functions. This formula is similar to others obtained previously by Hickerson and Mortenson, and by Mortenson and Zwegers. It is applied to the rank function, leading to an...
Gespeichert in:
| Veröffentlicht in: | The Ramanujan journal Jg. 65; H. 4; S. 1949 - 1970 |
|---|---|
| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer US
01.12.2024
|
| Schlagworte: | |
| ISSN: | 1382-4090, 1572-9303 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | A formula is established for the evaluation of double series of Hecke–Rogers type in terms of theta functions and Appell–Lerch functions. This formula is similar to others obtained previously by Hickerson and Mortenson, and by Mortenson and Zwegers. It is applied to the rank function, leading to an expansion closely analogous to two of Garvan’s double series identities. Several identities involving third-order mock theta functions are obtained as special cases. |
|---|---|
| AbstractList | A formula is established for the evaluation of double series of Hecke–Rogers type in terms of theta functions and Appell–Lerch functions. This formula is similar to others obtained previously by Hickerson and Mortenson, and by Mortenson and Zwegers. It is applied to the rank function, leading to an expansion closely analogous to two of Garvan’s double series identities. Several identities involving third-order mock theta functions are obtained as special cases. |
| Author | Bradley-Thrush, J. G. |
| Author_xml | – sequence: 1 givenname: J. G. surname: Bradley-Thrush fullname: Bradley-Thrush, J. G. email: jgbradleythrush@ciencias.ulisboa.pt organization: Grupo de Física Matemática, Instituto Superior Técnico, Universidade de Lisboa |
| BookMark | eNp9kM1KQzEQhYNUsK2-gKv7AtGZ_Hhzl1JqKxQE0XVIcyfaH3NL0orufAff0Cdpal27muFwvmHOGbBe7CIxdolwhQD1dUZE2XAQigMYJbg-YX3UteCNBNkruzSCK2jgjA1yXgKAAln32WT87tY7t110sepCNSW_op-v78fuhVKuMqUF5crFtqKPjYu52PLBt32lKrm4qsIu-gN8zk6DW2e6-JtD9nw3fhpN-exhcj-6nXEvlNhyXzttoK0dClImqNagE3DTOGqLrLWfI2HARqCWBudoioxBlgw4B1-THDJxvOtTl3OiYDdp8ebSp0WwhyrssQpbqrC_VVhdIHmEcjHHkswuu12K5c__qD2jg2Pb |
| Cites_doi | 10.1112/plms/s2-16.1.315 10.24033/asens.236 10.1090/S0002-9947-1986-0814916-2 10.1007/978-1-4614-0028-8_9 10.1090/S0002-9947-1984-0737878-3 10.1007/s11139-021-00445-4 10.1007/s11139-021-00530-8 10.1134/S0081543812010038 10.1007/BF01394279 10.1007/978-3-030-04480-0_10 10.1112/S0010437X09004060 10.1090/S0002-9947-1994-1243610-6 10.1007/s11139-014-9624-1 10.1112/plms/pdu007 10.1017/CBO9780511703096.011 10.1112/jlms/s1-11.1.55 10.1016/j.aim.2023.108944 |
| ContentType | Journal Article |
| Copyright | 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. |
| Copyright_xml | – notice: 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. |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s11139-024-00842-5 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1572-9303 |
| EndPage | 1970 |
| ExternalDocumentID | 10_1007_s11139_024_00842_5 |
| GroupedDBID | -5D -5G -BR -EM -Y2 -~C .86 .VR 06D 0R~ 0VY 123 1N0 1SB 203 29P 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5VS 67Z 6NX 6TJ 8TC 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADQRH ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGWIL AGWZB AGYKE AHAVH AHBYD AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z J9A JBSCW JCJTX JZLTJ KDC KOV LAK LLZTM M4Y MA- N2Q NB0 NPVJJ NQJWS NU0 O9- O93 O9J OAM OVD P9R PF0 PT4 PT5 QOS R89 R9I RIG RNI ROL RPX RSV RZC RZE RZK S16 S1Z S27 S3B SAP SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TEORI TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7U ZMTXR ~A9 AAPKM AAYXX ABBRH ABDBE ABFSG ABJCF ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFKRA AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA AZQEC BENPR BGLVJ CCPQU CITATION DWQXO GNUQQ HCIFZ M2P M7S PHGZM PHGZT PQGLB PTHSS |
| ID | FETCH-LOGICAL-c242t-c7a580d7a12e48f4d81a2069aed80d55cb1e1f19215381b18d801f33031b0c7e3 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001262885600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1382-4090 |
| IngestDate | Sat Nov 29 03:21:00 EST 2025 Fri Feb 21 02:36:10 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Keywords | Hecke–Rogers series Basic hypergeometric functions Appell–Lerch series 33D15 Theta functions |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c242t-c7a580d7a12e48f4d81a2069aed80d55cb1e1f19215381b18d801f33031b0c7e3 |
| PageCount | 22 |
| ParticipantIDs | crossref_primary_10_1007_s11139_024_00842_5 springer_journals_10_1007_s11139_024_00842_5 |
| PublicationCentury | 2000 |
| PublicationDate | 20241200 2024-12-00 |
| PublicationDateYYYYMMDD | 2024-12-01 |
| PublicationDate_xml | – month: 12 year: 2024 text: 20241200 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationSubtitle | An International Journal Devoted to the Areas of Mathematics Influenced by Ramanujan |
| PublicationTitle | The Ramanujan journal |
| PublicationTitleAbbrev | Ramanujan J |
| PublicationYear | 2024 |
| Publisher | Springer US |
| Publisher_xml | – name: Springer US |
| References | Garvan (CR14) 1988; 305 Garvan (CR15) 2015; 36 CR18 Bradley-Thrush (CR9) 2022; 57 Ramanujan (CR26) 1988 CR11 Kang (CR24) 2009; 145 CR10 Dyson (CR12) 1944; 8 CR30 Andrews (CR2) 1986; 293 Hickerson, Mortenson (CR22) 2014; 109 Frye, Garvan, Blümein, Schneider, Paule (CR13) 2019 Andrews (CR3) 2012; 276 Hickerson (CR21) 1988; 94 Rogers (CR28) 1917; 2 Andrews, Askey, Roy (CR4) 1999 Andrews, Berndt (CR5) 2009 Askey (CR7) 1987; 29 Whittaker, Watson (CR31) 1927 Heine (CR19) 1847; 34 CR29 Andrews (CR1) 1984; 283 Gordon, McIntosh, Alladi, Garvan (CR17) 2012 CR25 CR23 CR20 Appell (CR6) 1884; 3 Borwein, Borwein, Garvan (CR8) 1994; 343 Garvan (CR16) 2023; 61 Rogers (CR27) 1894; 25 DR Hickerson (842_CR22) 2014; 109 FJ Dyson (842_CR12) 1944; 8 842_CR10 S Ramanujan (842_CR26) 1988 842_CR30 842_CR11 842_CR18 LJ Rogers (842_CR28) 1917; 2 R Askey (842_CR7) 1987; 29 J Frye (842_CR13) 2019 E Heine (842_CR19) 1847; 34 FG Garvan (842_CR16) 2023; 61 SY Kang (842_CR24) 2009; 145 GE Andrews (842_CR4) 1999 842_CR20 JG Bradley-Thrush (842_CR9) 2022; 57 DR Hickerson (842_CR21) 1988; 94 842_CR25 GE Andrews (842_CR1) 1984; 283 842_CR23 JM Borwein (842_CR8) 1994; 343 842_CR29 B Gordon (842_CR17) 2012 FG Garvan (842_CR15) 2015; 36 LJ Rogers (842_CR27) 1894; 25 FG Garvan (842_CR14) 1988; 305 GE Andrews (842_CR3) 2012; 276 P Appell (842_CR6) 1884; 3 GE Andrews (842_CR5) 2009 GE Andrews (842_CR2) 1986; 293 ET Whittaker (842_CR31) 1927 |
| References_xml | – volume: 34 start-page: 285 year: 1847 end-page: 328 ident: CR19 article-title: Untersuchungen über die Reihe publication-title: J. Reine Angew. Math. – year: 1988 ident: CR26 publication-title: The Lost Notebook and Other Unpublished Papers – ident: CR18 – volume: 2 start-page: 315 issue: 16 year: 1917 end-page: 336 ident: CR28 article-title: On two theorems of combinatory analysis and allied identities publication-title: Proc. Lond. Math. Soc. doi: 10.1112/plms/s2-16.1.315 – volume: 305 start-page: 47 issue: 1 year: 1988 end-page: 77 ident: CR14 article-title: New combinatorial interpretations of Ramanujan’s partition congruences mod , and publication-title: Trans. Am. Math. Soc. – volume: 3 start-page: 135 issue: 1 year: 1884 end-page: 164 ident: CR6 article-title: Sur les fonctions doublement périodiques de troisième espèce publication-title: Ann. Sci. Éc. Norm. Supér. doi: 10.24033/asens.236 – volume: 25 start-page: 318 year: 1894 end-page: 343 ident: CR27 article-title: Second memoir on the expansion of certain infinite products publication-title: Proc. Lond. Math. Soc. – volume: 293 start-page: 113 issue: 1 year: 1986 end-page: 134 ident: CR2 article-title: The fifth and seventh order mock theta functions publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1986-0814916-2 – start-page: 95 year: 2012 end-page: 144 ident: CR17 article-title: A survey of classical mock theta functions publication-title: Partitions, q-Series, and Modular Forms, Developments in Mathematics doi: 10.1007/978-1-4614-0028-8_9 – volume: 283 start-page: 451 issue: 2 year: 1984 end-page: 458 ident: CR1 article-title: Hecke modular forms and the Kac-Peterson identites publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1984-0737878-3 – volume: 57 start-page: 291 issue: 1 year: 2022 end-page: 367 ident: CR9 article-title: Properties of the Appell–Lerch function (I) publication-title: Ramanujan J. doi: 10.1007/s11139-021-00445-4 – volume: 61 start-page: 545 issue: 2 year: 2023 end-page: 566 ident: CR16 article-title: A new approach to the Dyson rank conjectures publication-title: Ramanujan J. doi: 10.1007/s11139-021-00530-8 – ident: CR30 – ident: CR10 – volume: 276 start-page: 21 year: 2012 end-page: 32 ident: CR3 article-title: -Orthogonal polynomials, Rogers–Ramanujan identities, and mock theta functions publication-title: Proc. Steklov Inst. Math. doi: 10.1134/S0081543812010038 – volume: 8 start-page: 10 year: 1944 end-page: 15 ident: CR12 article-title: Some guesses in the theory of partitions publication-title: Eureka – volume: 94 start-page: 639 issue: 3 year: 1988 end-page: 660 ident: CR21 article-title: A proof of the mock theta conjectures publication-title: Invent. Math. doi: 10.1007/BF01394279 – start-page: 195 year: 2019 end-page: 258 ident: CR13 article-title: Automatic proof of theta-function identities publication-title: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, Texts and Monographs in Symbolic Computation doi: 10.1007/978-3-030-04480-0_10 – ident: CR29 – ident: CR25 – ident: CR23 – volume: 29 start-page: 101 issue: 2 year: 1987 end-page: 105 ident: CR7 article-title: Ramanujan’s and formal Laurent series publication-title: J. Indian Math. Soc. – year: 1999 ident: CR4 publication-title: Special Functions, Encyclopedia of Mathematics and its Applications – year: 1927 ident: CR31 publication-title: A Course of Modern Analysis – year: 2009 ident: CR5 publication-title: Ramanujan’s Lost Notebook. Part II – volume: 145 start-page: 553 issue: 3 year: 2009 end-page: 565 ident: CR24 article-title: Mock Jacobi forms in basic hypergeometric series publication-title: Compos. Math. doi: 10.1112/S0010437X09004060 – volume: 343 start-page: 35 year: 1994 end-page: 47 ident: CR8 article-title: Some cubic modular identities of Ramanujan publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1994-1243610-6 – ident: CR11 – volume: 36 start-page: 267 issue: 1–2 year: 2015 end-page: 296 ident: CR15 article-title: Universal mock theta functions and two-variable Hecke–Rogers identities publication-title: Ramanujan J. doi: 10.1007/s11139-014-9624-1 – volume: 109 start-page: 382 issue: 3 year: 2014 end-page: 422 ident: CR22 article-title: Hecke-type double sums, Appell–Lerch sums and mock theta functions. I publication-title: Proc. Lond. Math. Soc. doi: 10.1112/plms/pdu007 – ident: CR20 – volume: 94 start-page: 639 issue: 3 year: 1988 ident: 842_CR21 publication-title: Invent. Math. doi: 10.1007/BF01394279 – ident: 842_CR20 doi: 10.1017/CBO9780511703096.011 – volume: 343 start-page: 35 year: 1994 ident: 842_CR8 publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1994-1243610-6 – volume-title: The Lost Notebook and Other Unpublished Papers year: 1988 ident: 842_CR26 – start-page: 95 volume-title: Partitions, q-Series, and Modular Forms, Developments in Mathematics year: 2012 ident: 842_CR17 doi: 10.1007/978-1-4614-0028-8_9 – ident: 842_CR23 – ident: 842_CR29 doi: 10.1112/jlms/s1-11.1.55 – volume-title: Special Functions, Encyclopedia of Mathematics and its Applications year: 1999 ident: 842_CR4 – volume: 305 start-page: 47 issue: 1 year: 1988 ident: 842_CR14 publication-title: Trans. Am. Math. Soc. – volume: 145 start-page: 553 issue: 3 year: 2009 ident: 842_CR24 publication-title: Compos. Math. doi: 10.1112/S0010437X09004060 – volume: 34 start-page: 285 year: 1847 ident: 842_CR19 publication-title: J. Reine Angew. Math. – volume-title: Ramanujan’s Lost Notebook. Part II year: 2009 ident: 842_CR5 – volume: 61 start-page: 545 issue: 2 year: 2023 ident: 842_CR16 publication-title: Ramanujan J. doi: 10.1007/s11139-021-00530-8 – ident: 842_CR25 doi: 10.1016/j.aim.2023.108944 – ident: 842_CR11 – volume-title: A Course of Modern Analysis year: 1927 ident: 842_CR31 – volume: 57 start-page: 291 issue: 1 year: 2022 ident: 842_CR9 publication-title: Ramanujan J. doi: 10.1007/s11139-021-00445-4 – volume: 293 start-page: 113 issue: 1 year: 1986 ident: 842_CR2 publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1986-0814916-2 – volume: 276 start-page: 21 year: 2012 ident: 842_CR3 publication-title: Proc. Steklov Inst. Math. doi: 10.1134/S0081543812010038 – volume: 283 start-page: 451 issue: 2 year: 1984 ident: 842_CR1 publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1984-0737878-3 – ident: 842_CR30 – start-page: 195 volume-title: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, Texts and Monographs in Symbolic Computation year: 2019 ident: 842_CR13 doi: 10.1007/978-3-030-04480-0_10 – ident: 842_CR18 – volume: 109 start-page: 382 issue: 3 year: 2014 ident: 842_CR22 publication-title: Proc. Lond. Math. Soc. doi: 10.1112/plms/pdu007 – volume: 3 start-page: 135 issue: 1 year: 1884 ident: 842_CR6 publication-title: Ann. Sci. Éc. Norm. Supér. doi: 10.24033/asens.236 – volume: 25 start-page: 318 year: 1894 ident: 842_CR27 publication-title: Proc. Lond. Math. Soc. – volume: 29 start-page: 101 issue: 2 year: 1987 ident: 842_CR7 publication-title: J. Indian Math. Soc. – volume: 36 start-page: 267 issue: 1–2 year: 2015 ident: 842_CR15 publication-title: Ramanujan J. doi: 10.1007/s11139-014-9624-1 – ident: 842_CR10 – volume: 2 start-page: 315 issue: 16 year: 1917 ident: 842_CR28 publication-title: Proc. Lond. Math. Soc. doi: 10.1112/plms/s2-16.1.315 – volume: 8 start-page: 10 year: 1944 ident: 842_CR12 publication-title: Eureka |
| SSID | ssj0004037 |
| Score | 2.3338537 |
| Snippet | A formula is established for the evaluation of double series of Hecke–Rogers type in terms of theta functions and Appell–Lerch functions. This formula is... |
| SourceID | crossref springer |
| SourceType | Index Database Publisher |
| StartPage | 1949 |
| SubjectTerms | Combinatorics Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics Number Theory |
| Title | Evaluation of Hecke–Rogers series and expansions of the rank function |
| URI | https://link.springer.com/article/10.1007/s11139-024-00842-5 |
| Volume | 65 |
| WOSCitedRecordID | wos001262885600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1572-9303 dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0004037 issn: 1382-4090 databaseCode: M7S dateStart: 20241001 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1572-9303 dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0004037 issn: 1382-4090 databaseCode: BENPR dateStart: 20241001 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database customDbUrl: eissn: 1572-9303 dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0004037 issn: 1382-4090 databaseCode: M2P dateStart: 20241001 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest – providerCode: PRVAVX databaseName: Springer Journals customDbUrl: eissn: 1572-9303 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0004037 issn: 1382-4090 databaseCode: RSV dateStart: 19970301 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LSwMxEA5aPejBt_gmB28a2OwmbnIUae3FIvVBb0teC162pani0f_gP_SXOEl3Wwoi6G0Js9llMjNfXvMNQuemzDLGpCUKlheEmVzBU-6IpUJSzVMrhY7FJvJeTwwG8r5OCvPNbffmSDJG6nmyG4XZCgFMIYEEHpZQy2gF4E4Ed-w_PM-zIZPIlBnI9WB1JJM6VebnPhbhaPEsNEJMZ_N_P7eFNuopJb6e2sA2WnLVDlq_m_Gx-l10256ReuNhibsOfPfr47M_hC94HKzQeawqi907RIewgeaDHPSAQ1F3HNAvvLyHnjrtx5suqUsoEAPYOyGgey4SmyuaOiZKZgVVaXIllbPQzLnR1NEycKJB4KOaCmimMHzg6joxucv2UasaVu4AYc5LRS3PjHaOuZRqJpjIBDe5lrpM-SG6aDRZjKZMGcWcEzmopwD1FFE9BUhfNoosaq_xv4gf_U38GK2lYSzitZMT1JqMX90pWjVvkxc_Povm8g1vCLmi |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8NAEB60CurBt_h2D950IZvsms1RpLViW6RW6S1kH4FeUmmqePQ_-A_9Jc6mSUtBBL2FZbIJs_PY2Z35BuBcp0HAeWRoguEF5TpM8Cm01DAZMSV8E0lVNJsIOx3Z70cPZVFYXmW7V1eShaWeFbsx3K1Q9CnUgcBjCLUISxw9lkvk6z4-z6ohvQIp04HrYXQUeWWpzM9zzLuj-bvQwsU0Nv73c5uwXm4pyfVEBrZgwWbbsNae4rHmO3Bbn4J6k2FKmhZ19-vjszvEL-TESaHNSZIZYt_ROrgDtNzR4QzENXUnzvu5l3fhqVHv3TRp2UKBavS9Y4q8F9IzYcJ8y2XKjWSJ711FiTU4LIRWzLLUYaKh4WOKSRxmuHyo6srToQ32oJYNM7sPRIg0YUYEWlnLrc8Ul1wGUuhQRSr1xQFcVJyMXyZIGfEME9mxJ0b2xAV7YqS-rBgZl1qT_0J--DfyM1hp9tqtuHXXuT-CVd-tS5GCcgy18ejVnsCyfhsP8tFpITrfLfK8hg |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT8MwDLZgIAQH3og3OXCDaE2b0PSIgDEETBMv7VY1j0pcumktiCP_gX_IL8Hpuo1JCAlxqyInqWzHjpP4M8ChToOA88jQBMMLynWY4FdoqWEyYkr4JpKqLDYRtlqy04na37L4y9fuwyvJQU6DQ2nKinrPpPVx4hvDnQtF_0IdIDyGU9Mww13RIBev3z-NMyO9EjXTAe1hpBR5VdrMz2NMuqbJe9HS3TSW_v-jy7BYbTXJ6UA3VmDKZquwcDvCac3X4PJiBPZNuilpWlzTn-8fd12cLSdOO21OkswQ-4ZWwx2s5Y4ORyCu2DtxXtF1XofHxsXDWZNWpRWoRp9cUJSJkJ4JE-ZbLlNuJEt87yRKrMFmIbRilqUOKw0NIlNMYjNDsaIJUJ4ObbABtayb2U0gQqQJMyLQylpufaa45DKQQocqUqkvtuBoyNW4N0DQiMdYyY49MbInLtkTI_XxkKlxtZryX8i3_0Z-AHPt80Z8c9W63oF534mlfJmyC7Wi_2L3YFa_Fs95f7_Uoi_cHMVq |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Evaluation+of+Hecke%E2%80%93Rogers+series+and+expansions+of+the+rank+function&rft.jtitle=The+Ramanujan+journal&rft.au=Bradley-Thrush%2C+J.+G.&rft.date=2024-12-01&rft.pub=Springer+US&rft.issn=1382-4090&rft.eissn=1572-9303&rft.volume=65&rft.issue=4&rft.spage=1949&rft.epage=1970&rft_id=info:doi/10.1007%2Fs11139-024-00842-5&rft.externalDocID=10_1007_s11139_024_00842_5 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1382-4090&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1382-4090&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1382-4090&client=summon |