A "Proto-Pellet's Formula" for the M\"obius Function

Abstract

We give a short proof of "Pellet's Formula" for the M\"{o}bius Function on $\mathbb{F}_q[T]$, deriving an intermediate formula (which we call "Proto-Pellet's Formula") along the way. We then construct and prove an analogous "Proto-Pellet's Formula" for the M\"{o}bius Function for a number field (including the usual M\"{o}bius function on the integers).