无限环形本多项式乘积的常数性：以拉马纳和数为例
数论
2026-01-07 v2 组合数学
摘要
我们证明了无限乘积 其中 为第 个环形本多项式， 在单位圆盘内为常数。该证明将拉马纳关于拉马纳和数的结果（等价于素数定理）转化为无限乘积的语境中。我们还表明，拉马纳证明的类似恒等式导致了关于无限环形本多项式乘积的额外结果。
引用
@article{arxiv.2511.16975,
title = {Constancy of an Infinite Cyclotomic Product via Ramanujan Sums},
author = {Hartosh Singh Bal},
journal= {arXiv preprint arXiv:2511.16975},
year = {2026}
}
备注
v2 corrects the method of proof by replacing an unjustified interchange of infinite sums with a truncation-and-limit argument. All stated results are unchanged. The same correction applies to the proof as it appears in Integers 25 (2025), Article A96