Title:
Sonification of the Riemann zeta function
Sonification of the Riemann zeta function
Author(s)
Collins, Nick
Advisor(s)
Editor(s)
Collections
Supplementary to
Permanent Link
Abstract
The Riemann zeta function is one of the great wonders of mathematics, with a deep and still not fully solved connection to the prime numbers. It is defined via an infinite sum analogous to Fourier additive synthesis, and can be calculated in various ways. It was Riemann who extended the consideration of the series to complex number arguments, and the famous Riemann hypothesis states that the non-trivial zeroes of the function all occur on the critical line 0.5 + ti, and what is more, hold a deep correspondence with the prime numbers. For the purposes of sonification, the rich set of mathematical ideas to analyse the zeta function provide strong resources for sonic experimentation. The positions of the zeroes on the critical line can be directly sonified, as can values of the zeta function in the complex plane, approximations to the prime spectrum of prime powers and the Riemann spectrum of the zeroes rendered; more abstract ideas concerning the function also provide interesting scope.
Sponsor
Date Issued
2019-06
Extent
Resource Type
Text
Resource Subtype
Proceedings
Rights Statement
Licensed under Creative Commons Attribution Non-Commercial 4.0 International License.