Title:
Sonification of the Riemann zeta function
Sonification of the Riemann zeta function
| dc.contributor.author | Collins, Nick | |
| dc.contributor.corporatename | International Community for Auditory Display | |
| dc.date.accessioned | 2019-07-25T19:19:49Z | |
| dc.date.available | 2019-07-25T19:19:49Z | |
| dc.date.issued | 2019-06 | |
| dc.description | Presented at the 25th International Conference on Auditory Display (ICAD 2019) 23-27 June 2019, Northumbria University, Newcastle upon Tyne, UK. | |
| dc.description | Presented at the 25th International Conference on Auditory Display (ICAD 2019) 23-27 June 2019, Northumbria University, Newcastle upon Tyne, UK. | |
| dc.description.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. | |
| dc.identifier.doi | https://doi.org/10.21785/icad2019.003 | |
| dc.identifier.uri | http://hdl.handle.net/1853/61506 | |
| dc.publisher | Georgia Institute of Technology | |
| dc.publisher | Georgia Institute of Technology | |
| dc.publisher.original | International Community on Auditory Display | |
| dc.publisher.original | International Community for Auditory Display (ICAD) | |
| dc.relation.ispartofseries | International Conference on Auditory Display (ICAD) | |
| dc.rights | Licensed under Creative Commons Attribution Non-Commercial 4.0 International License. | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc/4.0/ | |
| dc.subject | Auditory display | |
| dc.subject | Reimann zeta | |
| dc.title | Sonification of the Riemann zeta function | |
| dc.type | Text | |
| dc.type.genre | Proceedings | |
| dspace.entity.type | Publication | |
| local.contributor.corporatename | Sonification Lab | |
| local.relation.ispartofseries | International Conference on Auditory Display (ICAD) | |
| relation.isOrgUnitOfPublication | 2727c3e6-abb7-4df0-877f-9f218987b22a | |
| relation.isSeriesOfPublication | 6cb90d00-3311-4767-954d-415c9341a358 |
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