Abstract First, we give a formula for the limiting value of the higher Mahler measures for general polynomials of one variable, which refines Biswas and Monico's result. Second, we give an analytic continuation of the zeta Mahler measures for polynomials of one variable to the whole complex plane as meromorphic functions, and we show that all of their poles are simple.

中文翻译：

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关于一个变量多项式的更高马勒测度和泽塔马勒测度

摘要 首先，我们给出了一个变量的一般多项式的较高马勒测度的极限值的公式，它改进了Biswas和Monico的结果。其次，我们将一个变量的多项式的 zeta Mahler 测度作为亚纯函数给出到整个复平面的解析延拓，并且我们证明了它们的所有极点都是简单的。