On a new proof of the Prime Number Theorem

Abstract: A new elementary proof of the prime number theorem presented recently in the framework of a scale invariant extension of the ordinary analysis is re-examined and clarified further. Both the formalism and proof are presented in a much more simplified manner. Basic properties of some key concepts such as infinitesimals, the associated nonarchimedean absolute values, invariance of measure and cardinality of a compact subset of the real line under an IFS are discussed more thoroughly. Some interesting applications of the formalism in analytic number theory are also presented. The error term as dictated by the Riemann hypothesis also follows naturally thus leading to an indirect proof of the hypothesis.