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Sonification of the Riemann Zeta Function

Collins, Nick

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Authors



Contributors

Paul Vickers
Editor

Matti Grohn
Editor

Tony Stockman
Editor

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). Sonification of the Riemann Zeta Function. In P. Vickers, M. Grohn, & T. Stockman (Eds.), Proceedings of the 25th International Conference on Auditory Display (ICAD 2019) (36-41). https://doi.org/10.21785/icad2019.003

Conference Name International Conference on Auditory Display
Conference Location Newcastle upon Tyne, England
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

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