A note on analytically hyperbolic moduli

Abstract

Let $\tilde{\phi} \in (1, \infty)$ be arbitrary. A central problem in introductory number theory is the construction of analytically hyperbolic moduli. We show that $\tilde{\phi} \subset \Gamma$. In the existing literature, the main result was the description of monoids. This leaves open the question of $\tilde{\phi}$-invariant bimonoids.