On $M$-functions for the value-distributions of $L$-functions
On $M$-functions for the value-distributions of $L$-functions
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关于$L$函数的值分布的$M$函数
DOI：
10.1007/s10986-019-09425-0
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发表时间：
2019
影响因子：
0.4
通讯作者：
Mine Masahiro
中科院分区：
文献类型：
--
作者：
稲富悠也;寒川義裕;Mine Masahiro;Mine Masahiro
玻尔和埃森证明了存在一定的极限值视为概率的价值黎曼zeta函数属于一个给定的区域在复杂的平面。他们还研究了概率的密度，自从Ihara和松本的研究以来，它被称为M函数。本文针对一类包含多种zeta函数和L函数的L函数的值分布构造了M函数。此外，我们改进了Bohr和Bohen关于极限收敛速度的估计。
Bohr and Jessen proved the existence of a certain limit value regarded as the probability that values of the Riemann zeta function belong to a given region in the complex plane. They also studied the density of the probability, which has been called theM-function since the studies of Ihara and Matsumoto. In this paper, we constructM-functions for the value-distributions ofL-functions in a class containing many kinds of zeta andL-functions. Moreover, we improve the estimate on the rate of the convergence of the limit studied by Bohr and Jessen.