Mertens' Proof of Mertens' Theorem

Details Mertens' Proof of Mertens' Theorem Mertens' Proof of Mertens' Theorem

2005-04-14

arxiv.org/abs/math/0504289v3

Mathematics

History and Overview

A modern proof of the Grossehilfsatz 2 added to Mertens' original proof. New biographical material on Mertens and new numerica

Scientific paper

We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit numerical error estimates and computations of the Mertens "constant," both of which are missing from modern expositions. In as much as his strategy and techniques are quite different from today's methods, his original methods deserve to be better known.

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