### Abstract

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.

Original language | English |
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Pages (from-to) | 125-138 |

Number of pages | 14 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 445 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2017 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

**An ergodic value distribution of certain meromorphic functions.** / Lee, Junghun; Ade Irma, Suriajaya.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 445, no. 1, pp. 125-138. https://doi.org/10.1016/j.jmaa.2016.07.064

}

TY - JOUR

T1 - An ergodic value distribution of certain meromorphic functions

AU - Lee, Junghun

AU - Ade Irma, Suriajaya

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84984824050&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84984824050&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2016.07.064

DO - 10.1016/j.jmaa.2016.07.064

M3 - Article

AN - SCOPUS:84984824050

VL - 445

SP - 125

EP - 138

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -