Spectral Analysis of the $D_{\log }^{}$ Operators

This paper investigates the recent Connes-Consani-Moscovici $D_{\log }^{}$ operators, whose spectra are currently hypothesized to approach the zeros of $\zeta (\frac{1}{2}+is)$ as $\lambda ,N\to \mathrm{\infty }$. It turns out that when considering different standard notions of error, the dissonance between the spectra and Riemann $\zeta$ zeros either appears to or can be proven to be inverse logarithmic in nature, which elegantly fits the distribution of prime numbers.