Cors

This is for my original known ancestor, a sailor-trader in New Amsterdam, in the 1630s-1650s, who was born around 1612, in/around a hamlet called Langeraar (or Langeraer) near Leiden, Suid Holland.

His full name was Cors Pieters, or Piters, or Pietersz, or even Pieterszen, depending upon which referenced records that remain of the scribe(s) for the Provincial Secretaries of New Netherlands. A few times, translators (in the last hundred sixty years or so) have called him Cornelius, but that may not be a correct assumption; I've also seen reference to it being a stand-alone name (not a diminutive), or a diminutive of Kerstiaan (Christiaan). I'm hoping that I can get consensus and possibly some reference scholarship on the derivation of this name, and any other history.