论文标题
在原始数字字段上的单位方程式上
On the unit equation over cyclic number fields of prime degree
论文作者
论文摘要
令$ \ ell \ ne 3 $为素数。我们表明，只有许多环数字段$ f $ f $ $ \ ell $，单位方程$$λ+μ= 1，\qquadλ，〜μ \ in \ mathcal {o} _f^\ times $ $ $ times $$有解决方案。我们的结果是有效的。例如，我们推断出，单位方程的解决方案为$ \ mathbb {q}}（ζ_{11}）^+$的唯一循环Quintic数字字段。
Let $\ell \ne 3$ be a prime. We show that there are only finitely many cyclic number fields $F$ of degree $\ell$ for which the unit equation $$λ+ μ= 1, \qquad λ,~μ\in \mathcal{O}_F^\times$$ has solutions. Our result is effective. For example, we deduce that the only cyclic quintic number field for which the unit equation has solutions is $\mathbb{Q}(ζ_{11})^+$.
