关于3n-收敛的和范围
On Sum Ranges for $3n$-convergence
- Iowa State University（爱荷华州立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究将无穷级数重排概念扩展到3n-收敛，证明了3n-和范围仍为子群的情形及非子群的情形，揭示了3n-收敛的深层特性。
AI中文摘要：
黎曼重排定理（RRT）指出无穷级数的交换性与有限级数存在差异。我们希望将无穷级数重排的概念扩展到更弱的收敛形式，如仅对每2个或每3个索引的部分级数收敛，即2n-或3n-收敛。对于2n-收敛，已有研究表明其和范围与RRT中的标准情形共同构成实数的平移加法子群。本文中，我们证明3n-和范围仍为子群的情形，以及3n-和范围不能为子群的情形，揭示了3n-收敛的更深层性质。
英文摘要：
The Riemann Rearrangement Theorem (RRT) tells us that commutativity of infinite series can differ from finite series. We wish to extend the notion of infinite series rearrangements to weaker forms of convergence, such as partial series convergence on every 2nd or 3rd index, called $2n$- or $3n$-convergence. In the case of $2n$-convergence, it has been shown that the sum range, along with the standard cases in the RRT, can produce a shifted additive subgroup of reals. In this paper, we show cases where the $3n$-sum range is still a subgroup and a case where the $3n$-sum range cannot be a subgroup, proving the existence of more depth for $3n$-convergence.
