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The Riemann Hypothesis
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2013 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

The Riemann hypothesis was first proposed by Bernhard Riemann in 1860 [1] and says all

non-trivial zeroes to the Riemann zeta function lie on the line with the real part


in the

complex plane [1]. If proven to be true this would give a much better approximation of the

number of prime numbers less than some number X.

The Riemann hypothesis is regarded to be one of the most important unsolved mathematical

problems. It is one of the Clay InstituteMilleniumproblems and originally one of the unsolved

problems presented by David Hilbert as essential for 20th century mathematics at International

Congress ofMathematics in 1900.

It is the aim of this report to illustrate how the zeros to the zeta function affects the approximation

of the number of primes less than X.

We will start out by defining some core concepts in chapters 2,3 and 4 and then move on

to some theory about integral functions of order 1. This theory will then be applied a function

of interest. We then move on and use the results to derive the prime number theorem.

Place, publisher, year, edition, pages
2013. , 29 p.
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-127725OAI: diva2:645796
Available from: 2013-09-05 Created: 2013-09-05 Last updated: 2013-09-05Bibliographically approved

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