# An ergodic value distribution of certain meromorphic functions

1 引用 (Scopus)

### 抄録

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 and L-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.

元の言語 英語 125-138 14 Journal of Mathematical Analysis and Applications 445 1 https://doi.org/10.1016/j.jmaa.2016.07.064 出版済み - 1 1 2017 Yes

### Fingerprint

Value Distribution
Meromorphic Function
Mean Value
Riemann zeta function
Ergodic Theorem
L-function
Equivalence
Transform
Calculate

### All Science Journal Classification (ASJC) codes

• Analysis
• Applied Mathematics

### これを引用

：: Journal of Mathematical Analysis and Applications, 巻 445, 番号 1, 01.01.2017, p. 125-138.

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