# An ergodic value distribution of certain meromorphic functions

Source: [An ergodic value distribution of certain meromorphic functions](<https://www.sota2.com/research/paper/68fa587a1e209131ce9aeb4e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T15:21:36.715Z

Authors: Junghun Lee, Ade Irma Suriajaya

Published: 2015-12-14T04:37:46.000Z

## 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 Lindel\\"{o}f hypothesis of the Riemann zeta function in terms of its certain ergodic value distribution associated with affine Boolean transformations.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1512.04169>)

[PDF](<https://arxiv.org/pdf/1512.04169.pdf>)