On an spt function for the $4$-th symmetrized crank function
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914143611650048 |
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| author | Patkowski, Alexander E. |
| author_facet | Patkowski, Alexander E. |
| contents | In this paper we find the smallest part function related to the $4$-th symmetrized crank function, corresponding to the one obtained in Patkowski [11] for the $4$-th symmetrized rank function. This provides us with a direct relationship with Garvan's second order smallest part function. We obtain some congruences for these $spt$ functions, as well as asymptotics and inequalities. A finite $q$-series which generates an $spt$ function related to the second crank moment is also stated. This identity has an important relationship to the one obtained by Patkowski [12] related to the second rank moment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On an spt function for the $4$-th symmetrized crank function Patkowski, Alexander E. Number Theory In this paper we find the smallest part function related to the $4$-th symmetrized crank function, corresponding to the one obtained in Patkowski [11] for the $4$-th symmetrized rank function. This provides us with a direct relationship with Garvan's second order smallest part function. We obtain some congruences for these $spt$ functions, as well as asymptotics and inequalities. A finite $q$-series which generates an $spt$ function related to the second crank moment is also stated. This identity has an important relationship to the one obtained by Patkowski [12] related to the second rank moment. |
| title | On an spt function for the $4$-th symmetrized crank function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.05857 |