Anomalous Partial Quotients in the Continued Fraction of $\sqrt{\hat{I}\P (3)-S_N}$

David Victor Feldman

Let $S_N={\sum }_{j=1}^N{j}^{-3}$ and $R_N=\hat{I}\P (3)-S_N$. The simple continued fraction of $\sqrt{R_N}$ has partial quotients of generic size $O(N)$. We prove that at the sequence o…