Exact formulae for ranks of partitions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912832330661888 |
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| author | Sun, Qihang |
| author_facet | Sun, Qihang |
| contents | In 2009, Bringmann arXiv:0708.0691 [math.NT] used the circle method to prove an asymptotic formula for the Fourier coefficients of rank generating functions. In this paper, we prove that Bringmann's formula, when summing up to infinity and in the case of prime modulus, gives a Rademacher-type exact formula involving sums of vector-valued Kloosterman sums. As a corollary, in another paper arXiv:2406.07469 [math.NT], we will provide a new proof of Dyson's conjectures by showing that the certain Kloosterman sums vanish. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06294 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact formulae for ranks of partitions Sun, Qihang Number Theory 11P82, 11L05, 11F20, 11F37 In 2009, Bringmann arXiv:0708.0691 [math.NT] used the circle method to prove an asymptotic formula for the Fourier coefficients of rank generating functions. In this paper, we prove that Bringmann's formula, when summing up to infinity and in the case of prime modulus, gives a Rademacher-type exact formula involving sums of vector-valued Kloosterman sums. As a corollary, in another paper arXiv:2406.07469 [math.NT], we will provide a new proof of Dyson's conjectures by showing that the certain Kloosterman sums vanish. |
| title | Exact formulae for ranks of partitions |
| topic | Number Theory 11P82, 11L05, 11F20, 11F37 |
| url | https://arxiv.org/abs/2406.06294 |