关于与Catalan常数相关的两类周期积分
On two families of period integrals related to Catalan's constant
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中文总结 AI 辅助
本文研究由Catalan常数混合动机构造产生的3参数周期积分族，证明其与Rivoal等人考虑的超几何周期积分族密切相关。
中文摘要 AI 辅助
在文献[arXiv:2510.20648]中，与Catalan常数$G=\sum_{n=0}^\infty (-1)^n/(2n+1)^2$相关联的混合动机的构造，产生了一系列周期积分，这些积分可求值为1和$G$的线性形式。在此系列中，积分区域的边界引出了一个自然的3参数周期积分族。我们证明该族与Rivoal、Zudilin和Nesterenko先前考虑的超几何周期积分族密切相关。
英文摘要
The construction of a mixed motive associated with Catalan's constant $G=\sum_{n=0}^\infty (-1)^n/(2n+1)^2$ in [arXiv:2510.20648] led to a supply of period integrals that evaluate to linear forms in 1 and $G$. Inside this supply, the boundary of the integration domain leads to a natural 3-parameter family of period integrals. We show that this family is closely related to the family of hypergeometric period integrals considered earlier by Rivoal, Zudilin and Nesterenko.
发表机构
- University of Winnipeg（温尼伯大学）
机构由 AI 辅助整理，请以论文原文为准。
