AI 中文总结
本文建立归纳论证，证明无穷序列无平方因子阶循环群上的Fuglede猜想，对所有这类群证明了tile-to-spectral方向，对素因子快速增长的群证明了spectral-tiling方向，填补了此前无任意多不同因子的循环群猜想成立的空白。
AI 中文摘要
本文的主要结果是建立了一个归纳论证，用以证明无穷序列无平方因子阶循环群上的Fuglede猜想。该猜想的“ tile-to-spectral”方向对所有无平方因子循环群成立，而我们仅对其中素因子快速增长的群证明了“spectral-tiling”方向。为实现这一点，我们开发了一种归纳技术，其根源在于作者与Fallon、Kiss、Mayeli合作的一篇先前论文。根据近期预印本，Fuglede猜想仅对有限循环群仍未解决，且此前，不存在已知的具有任意多个不同因子的循环群，其猜想成立。
英文摘要
The main result of the paper is that an inductive argument is established to prove the Fuglede's conjecture for an infinite sequence of square-free order cyclic groups. The tile-to-spectral direction of the conjecture holds for all square-free cyclic groups, whereas we prove the spectral-tiling direction only for those groups among them whose prime factors grow rapidly. To achieve this, we develop an inductive technique with roots in a previous paper by the author co-authored with Fallon, Kiss, and Mayeli. Following recent preprints, Fuglede's conjecture remains open only for finite cyclic groups, and until now, there was no cyclic group for which the conjecture was known that possessed an arbitrary number of distinct divisors.
