An ergodic value distribution of certain meromorphic functions
An ergodic value distribution of certain meromorphic functions
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某些亚纯函数的遍历值分布
DOI：
10.1016/j.jmaa.2016.07.064
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Ade Irma Suriajaya
中科院分区：
文献类型：
--
作者：
Junghun Lee;Ade Irma Suriajaya
我们通过使用特定的遍历变换（我们称之为仿射布尔变换）来计算亚纯函数的某个均值。我们使用Birkhoff的遍历定理将平均值转化为一个可计算的积分，使我们能够完全确定这种遍历类型的平均值。作为例子，我们介绍了zeta函数和L-函数的一些应用。我们还证明了一个等价的Lindelöf假设的黎曼zeta函数在其一定的遍历值分布与仿射布尔变换。
We calculate a certain mean-value of meromorphic functions by using specific ergodic transformations, which we call affine Boolean transformations. We use Birkhoff's ergodic theorem to transform the mean-value into a computable integral which allows us to completely determine the mean-value of this ergodic type. As examples, we introduce some applications to zeta functions andL-functions. We also prove an equivalence of the Lindelöf hypothesis of the Riemann zeta function in terms of its certain ergodic value distribution associated with affine Boolean transformations.