On the Non p-Rationality and Iwasawa Invariants of Certain Real
Quadratic Fields
On the Non p-Rationality and Iwasawa Invariants of Certain Real
Quadratic Fields
Let $p$ be an odd prime, and $m,r \in \mathbb{Z}^+$ with $m$ coprime to $p$. In this paper we investigate the real quadratic fields $K = \mathbb{Q}(\sqrt{m^2p^{2r} + 1})$. We first show that for $m < C$, where constant $C$ depends on $p$, the fundamental unit $\varepsilon$ of $K$ satisfies …