Mean values of multiplicative functions over function fields
Mean values of multiplicative functions over function fields
复制标题
函数域上乘法函数的平均值
DOI：
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发表时间：
2015
影响因子：
0.8
通讯作者：
K. Soundararajan
中科院分区：
文献类型：
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作者：
A. Granville;Adam J. Harper;K. Soundararajan
讨论了函数域上乘法函数的均值。特别地，我们将作者对Halász的均值定理的新证明适应于这个更简单的设置。在函数域的设置中，整数上出现的一些技术困难消失了，这有助于更清楚地揭示数域证明的主要思想。我们还得到了Lipschitz估计，它显示了乘法函数在函数域上的平均值的缓慢变化，它显示了在整数情况下不存在的一些特征。
We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors’ new proof of Halász’s theorem on mean values to this simpler setting. Several of the technical difficulties that arise over the integers disappear in the function field setting, which helps bring out more clearly the main ideas of the proofs over number fields. We also obtain Lipschitz estimates showing the slow variation of mean values of multiplicative functions over function fields, which display some features that are not present in the integer situation.