An ergodic value distribution of certain meromorphic functions
Number Theory
2021-09-21 v4
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 -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.
Cite
@article{arxiv.1512.04169,
title = {An ergodic value distribution of certain meromorphic functions},
author = {Junghun Lee and Ade Irma Suriajaya},
journal= {arXiv preprint arXiv:1512.04169},
year = {2021}
}