2011/03/30 by Dhurjati Prasad Datta, Datta, Dhurjati Prasad · 1 citation
Mathematics · Physics and Astronomy · #History and Theory of Mathematics #Mathematical and Theoretical Analysis #Quantum Mechanics and Applications #math.GM #msc:11A41 #msc:26A12
paper · pdf · doi:10.48550/arxiv.1103.6176
Completed originally on October 2010, this is a revised and extended version on the basis of a referee report received sometime in December 2010, currently still under referee evaluation
arxiv created 2011/03/30 · arxiv updated 2011/04/01
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.