与Rogers-Ramanujan连分数相关的三参数模函数族的Eta商表示
Eta-Quotient Representations for a Three Parameter Family of Modular Functions Associated with the Rogers-Ramanujan Continued Fraction
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中文总结 AI 辅助
本文构造了与Rogers-Ramanujan连分数相关的三参数模函数族，推导其递归eta商表示，并应用于剖分公式，特别是用于获得受限奇数差分拆的5-剖分公式。
中文摘要 AI 辅助
2021年，Chern和Tang引入了与Rogers-Ramanujan连分数相关的两个双参数模函数族。他们建立了将这些族的成员用eta商表示的递推关系，并利用这些表达式获得了剖分公式。受他们工作的启发，我们构造了一个三参数扩展，并推导了相应的递归eta商表示。我们的结果也对剖分公式有应用。特别地，它被用于另一项工作中，以获得具有受限奇数差的分拆的5-剖分公式。
英文摘要
In 2021, Chern and Tang introduced two families of two-parameter modular functions associated with the Rogers-Ramanujan continued fraction. They established recurrence relations that express the members of these families in terms of eta quotients, and used these expressions to obtain dissection formulas. Motivated by their work, we construct a three-parameter extension and derive the corresponding recursive eta quotient representations. Our result also has applications to dissection formulas. In particular, it is used in separate work to obtain $5$-dissection formulas for overpartitions with restricted odd differences.
发表机构
- University of Minnesota Duluth（明尼苏达大学德卢斯分校）
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