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O'Rourke, Ciaran (2013) The prime number theorem: Analytic and elementary proofs. Masters thesis, National University of Ireland Maynooth.
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Abstract
Three proofs of the prime number theorem are presented. The rst is a heavily analytic
proof based on early accounts. Cauchy's residue theorem and various results relating to the
Riemann zeta function play a vital role. A weaker result than the prime number theorem
is used for the proof, namely Chebyshev's theorem. The second proof is elementary in the
sense that it involves no complex analysis. Instead, mainly number-theoretic results are
used, in particular, Selberg's formulas. The third proof, like the rst, relies heavily on the
Riemann zeta function, but is considerably shorter for the use of the Laplace transform and
the analytic theorem.
| Item Type: | Thesis (Masters) |
|---|---|
| Keywords: | prime number theorem; analytic and elementary proofs; |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 4470 |
| Depositing User: | IR eTheses |
| Date Deposited: | 11 Sep 2013 14:33 |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/4470 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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