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arXiv · 1512.04169

An ergodic value distribution of certain meromorphic functions

Junghun Lee·Ade Irma Suriajaya
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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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Junghun Lee, Ade Irma Suriajaya. 2015-12-14. An ergodic value distribution of certain meromorphic functions. https://doi.org/10.1016/j.jmaa.2016.07.064

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