Algebraic proof for the independence of the 2-power cyclotomic units

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发表日期：

2025年11月12日

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Rintaro Kozuma

摘要

We present a new proof for the multiplicative independence of cyclotomic units in the $p^n$ $p^{n}$ -th cyclotomic field for $p=2$ $p = 2$ and for any integer $n \ge 3$ $n \geq 3$ , without relying on the non-vanishing property of L-functions. In addition, our approach yields some results applicable to an arbitrary prime p.