An ergodic value distribution of certain meromorphic functions

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.

Cited by in corpus (2)

• On good universality and the Riemann hypothesis
• Limit Theorems for a class of unbounded observables with an application to "Sampling the Lindelöf hypothesis"