English

Level $17$ Ramanujan-Sato series

Number Theory 2017-11-02 v1

Abstract

Two level 17 modular functions r=q2n=1(1qn)(n17),s=q2n=1(1q17n)3(1qn)3, r=q^{2}\prod_{n=1}^{\infty}(1-q^{n})^{\left(\frac{n}{17}\right)},\quad s=q^{2}\prod_{n=1}^{\infty}\frac{(1-q^{17n})^{3}}{(1-q^{n})^{3}}, are used to construct a new class of Ramanujan-Sato series for 1/π1/\pi. The expansions are induced by modular identities similar to those level of 5 and 13 appearing in Ramanujan's Notebooks. A complete list of rational and quadratic series corresponding to singular values of the parameters is derived.

Keywords

Cite

@article{arxiv.1711.00459,
  title  = {Level $17$ Ramanujan-Sato series},
  author = {Tim Huber and Dan Schultz and Dongxi Ye},
  journal= {arXiv preprint arXiv:1711.00459},
  year   = {2017}
}

Comments

15 pages

R2 v1 2026-06-22T22:33:19.380Z