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SCALE-FREE ANALYSIS AND THE PRIME NUMBER THEOREM

DHURJATI PRASAD DATTA

Department of Mathematics, University of North Bengal, Siliguri, West Bengal, Pin: 734013, India

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and

ANUJA ROY CHOUDHURI

Ananda Chandra College, Jalpaiguri-735101, India

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https://doi.org/10.1142/S0218348X10004853Cited by:3 (Source: Crossref)

Abstract

We present an elementary proof of the prime number theorem. The relative error follows a golden ratio scaling law and respects the bound obtained from the Riemann's hypothesis. The proof is derived in the framework of a scale-free nonarchimedean extension of the real number system exploiting the concept of relative infinitesimals introduced recently in connection with ultramemtric models of Cantor sets. The extended real number system is realized as a completion of the field of rational numbers Q under a new non-archimedean absolute value, which treats arbitrarily small and large numbers separately from a finite real number.

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