The fundamental unit of $\Z[\sqrt{N}]$ for square-free $N=5 mod 8$ is either $\epsilon$ or $\epsilon^3$ where $\epsilon$ denotes the fundamental unit of the maximal order of $\Q(\sqrt{N})$. We give infinitely many examples for each case.
New characterization of the norm of the fundamental unit of $\mathbb{Q}(\sqrt M)$
On certain families of Drinfeld quasi-modular forms
Maximal order for divisor functions and zeros of the Riemann zeta-function
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