The issue had been raised whether the function $z + z^2 + \cdots + z^{2n}, sometimes called Fredholm series, has infinitely many zeroes in the unit disk. We provide an affirmative answer, proving that in fact every complex number occurs as a value infinitely many times, even restricting the function to any open set meeting the unit circle.

中文翻译：

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关于Fredholm系列零点的注释

已经提出了一个问题，即函数$ z + z ^ 2 + \ cdots + z ^ {2n}（有时称为Fredholm级数）在单位磁盘中是否具有无限多个零。我们提供一个肯定的答案，证明实际上每个复数都会作为一个值无限次出现，甚至将函数限制为任何满足单位圆的开放集。