Sonification of the Riemann Zeta Function

Collins, Nick

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.

Citation

Collins, N. (2019, June). Sonification of the Riemann Zeta Function. Presented at International Conference on Auditory Display, Newcastle upon Tyne, England

• Presentation Conference Type: Conference Paper (published)
• Conference Name: International Conference on Auditory Display
• End Date: Jun 27, 2019
• Acceptance Date: May 6, 2019
• Publication Date: 2019
• Deposit Date: May 15, 2019
• Publicly Available Date: May 15, 2019
• Pages: 36-41
• Book Title: Proceedings of the 25th International Conference on Auditory Display (ICAD 2019).
• DOI: https://doi.org/10.21785/icad2019.003
• Public URL: https://durham-repository.worktribe.com/output/1144201