论文标题
在具有小部分总和的乘法函数上
On multiplicative functions with small partial sums
论文作者
论文摘要
在分析数理论中，有几种结果利用有关乘法函数的质量值的信息，以提取有关其平均值的信息。此类结果的示例包括Wirsing的定理和Landau-Selberg-Delange方法。在本文中，我们对相反的方向感兴趣。 In particular, we prove that when $f$ is a suitable divisor-bounded multiplicative function with small partial sums, then $f(p)\approx-p^{iγ_1}-\ldots-p^{iγ_m}$ on average, where the $γ_j$'s are the imaginary parts of the zeros of the Dirichet series of $f$ on the line $\Re(s)=1$.这扩展了Koukoulopoulos和Soundararajan的结果，它基于Koukoulopoulos先前作品的想法，而$ | f | f | \ leqslant 1 $。
In analytic number theory, several results make use of information regarding the prime values of a multiplicative function in order to extract information about its averages. Examples of such results include Wirsing's theorem and the Landau-Selberg-Delange method. In this paper, we are interested in the opposite direction. In particular, we prove that when $f$ is a suitable divisor-bounded multiplicative function with small partial sums, then $f(p)\approx-p^{iγ_1}-\ldots-p^{iγ_m}$ on average, where the $γ_j$'s are the imaginary parts of the zeros of the Dirichet series of $f$ on the line $\Re(s)=1$. This extends a result of Koukoulopoulos and Soundararajan and it builds upon ideas coming from previous work of Koukoulopoulos for the case where $|f|\leqslant 1$.
