arXiv Open Access 2024

Exact formulae for ranks of partitions

Qihang Sun

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

math.NT

Penulis (1)

Qihang Sun

Format Sitasi

APA MLA BibTeX

Sun, Q. (2024). Exact formulae for ranks of partitions. https://arxiv.org/abs/2406.06294

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓