New congruences for fractional powers of the generating function for the partition function
Recently, Chan and Wang [2] studied the coefficients of qn in the series of expansion of (∏n=1∞(1 - qn))k, | q | < 1 when k is a rational number which is denoted by pk(n). In particular, they proved many congruences satisfied by pk(n) and conjectured modulo 192 congruences for pk(n). Motivated by...
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AIP Conference Proceedings
2022
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| author | Isnaini, Uha Hong, Nankun |
| author_facet | Isnaini, Uha Hong, Nankun |
| author_sort | Isnaini, Uha |
| collection | UGM |
| description | Recently, Chan and Wang [2] studied the coefficients of qn in the series of expansion of (∏n=1∞(1 - qn))k, | q | < 1 when k is a rational number which is denoted by pk(n). In particular, they proved many congruences satisfied by pk(n) and conjectured modulo 192 congruences for pk(n). Motivated by their work, we studied some modulo l2 congruences for pk(n) when l is a prime. We proved congruences for p-1/b(n) when (b, l) = (3,19), (4, 17), (5, 31), (6,17) and (7, 29).f 2II We note that a conjecture in [2] is a special case when (b, l) = (3, 19) |
| first_indexed | 2024-03-14T00:10:24Z |
| format | Other |
| id | oai:generic.eprints.org:284469 |
| institution | Universiti Gadjah Mada |
| last_indexed | 2024-03-14T00:10:24Z |
| publishDate | 2022 |
| publisher | AIP Conference Proceedings |
| record_format | dspace |
| spelling | oai:generic.eprints.org:2844692024-01-04T07:14:43Z https://repository.ugm.ac.id/284469/ New congruences for fractional powers of the generating function for the partition function Isnaini, Uha Hong, Nankun Pure Mathematics Recently, Chan and Wang [2] studied the coefficients of qn in the series of expansion of (∏n=1∞(1 - qn))k, | q | < 1 when k is a rational number which is denoted by pk(n). In particular, they proved many congruences satisfied by pk(n) and conjectured modulo 192 congruences for pk(n). Motivated by their work, we studied some modulo l2 congruences for pk(n) when l is a prime. We proved congruences for p-1/b(n) when (b, l) = (3,19), (4, 17), (5, 31), (6,17) and (7, 29).f 2II We note that a conjecture in [2] is a special case when (b, l) = (3, 19) AIP Conference Proceedings 2022 Other NonPeerReviewed Isnaini, Uha and Hong, Nankun (2022) New congruences for fractional powers of the generating function for the partition function. AIP Conference Proceedings. https://pubs.aip.org/aip/acp/article-abstract/2575/1/020004/2830197/New-congruences-for-fractional-powers-of-the?redirectedFrom=fulltext doi.org/10.1063/5.0108174 |
| spellingShingle | Pure Mathematics Isnaini, Uha Hong, Nankun New congruences for fractional powers of the generating function for the partition function |
| title | New congruences for fractional powers of the generating function for the partition function |
| title_full | New congruences for fractional powers of the generating function for the partition function |
| title_fullStr | New congruences for fractional powers of the generating function for the partition function |
| title_full_unstemmed | New congruences for fractional powers of the generating function for the partition function |
| title_short | New congruences for fractional powers of the generating function for the partition function |
| title_sort | new congruences for fractional powers of the generating function for the partition function |
| topic | Pure Mathematics |
| work_keys_str_mv | AT isnainiuha newcongruencesforfractionalpowersofthegeneratingfunctionforthepartitionfunction AT hongnankun newcongruencesforfractionalpowersofthegeneratingfunctionforthepartitionfunction |