Mertens' Proof of Mertens' Theorem
| dc.creator | Villarino, Mark B. | |
| dc.date | 2005-04-14 | |
| dc.date | 2005-05-17 | |
| dc.date.accessioned | 2026-07-07T05:19:07Z | |
| dc.date.available | 2026-07-07T05:19:07Z | |
| dc.description | 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. | |
| dc.description | A modern proof of the Grossehilfsatz 2 added to Mertens' original proof. New biographical material on Mertens and new numerical table on the accuracy of the error term. Many improvements of details | |
| dc.identifier | https://arxiv.org/abs/math/0504289 | |
| dc.identifier | http://arxiv.org/abs/math/0504289 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74898 | |
| dc.subject | History and Overview | |
| dc.subject | Number Theory | |
| dc.subject | 01A55,11N05 | |
| dc.title | Mertens' Proof of Mertens' Theorem | |
| dc.type | text |