中文

解释拉马努金致哈代最后一封信中的“未闭合”评论

数论 2016-01-05 v3

摘要

我们研究 qq-级数 F(q)=qm(m+1)/2/(q)m2F(q) = \sum q^{m(m+1)/2}/(q)_m^2,并就拉马努金为何可能认为 F(q)F(q) 不“闭合”提供一些评论。

关键词

引用

@article{arxiv.1512.07436,
  title  = {Explaining Ramanujan's "Unclosed" Comment in His Last Letter to Hardy},
  author = {Daniel Parry},
  journal= {arXiv preprint arXiv:1512.07436},
  year   = {2016}
}

备注

Typo Log V2: fixed typo of summation index n->j on page 12 V3: Fixed minus sign error on $m$ in Remark 1. V3: Orphan n->j change on Equation 3.7 fixed. V3: Deleted extra ) in equation (4.2). V3: Fixed mistake with the variable transformation $\sqrt[4]{5}\to 1/\sqrt{4]{5}$ throughout the manuscript V3: Added more context to the dot product computation