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An application of Tauber theory: proving the Prime Number Theorem

Koolstra, Jori (2018) An application of Tauber theory: proving the Prime Number Theorem. Bachelor's Thesis, Mathematics.

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Abstract

We look at the origins of Tauber theory, and apply it to prove the prime number theorem (PNT). Specifically, we prove a weak version of the Wiener-Ikehara Tauberian theorem due to Newman. Its application requires us to establish some properties of the Riemann zeta function. Most notably with regard to its meromorphic continuation, and the distribution of its zeros.

Item Type: Thesis (Bachelor's Thesis)
Supervisor:
Supervisor nameSupervisor E mail
Top, J.J.Top@rug.nl
Sterk, A.E.A.E.Sterk@rug.nl
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 06 Jul 2018
Last Modified: 10 Jul 2018 06:17
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/17647

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