Phase Portraits of Bi-dimensional Zeta Values

In this extended abstract, we present how to compute and visualize phase portraits of bi-dimensional Zeta Values. Such technology is useful to explore bi-dimensional Zeta Values and in long-term quest to discover a 2D-Riemann hypothesis. To reach this goal, we need two preliminary steps: [Formula: s...

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Detalles Bibliográficos
Autor principal: Bouillot, Olivier
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340897/
http://dx.doi.org/10.1007/978-3-030-52200-1_39
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author Bouillot, Olivier
author_facet Bouillot, Olivier
author_sort Bouillot, Olivier
collection PubMed
description In this extended abstract, we present how to compute and visualize phase portraits of bi-dimensional Zeta Values. Such technology is useful to explore bi-dimensional Zeta Values and in long-term quest to discover a 2D-Riemann hypothesis. To reach this goal, we need two preliminary steps: [Formula: see text] the notion of phase portraits and a general tool to visualize phase portrait based on interactive Jupyter widgets. [Formula: see text] the ability to compute numerical approximations of bi-dimensional Zeta values, using mpmath, a Python library for arbitrary-precision floating-point arithmetic. To this end, we develop a theory to numerically compute double sums and produce the first algorithm to compute bi-dimensional Zeta Values with complex parameters.
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spelling pubmed-73408972020-07-08 Phase Portraits of Bi-dimensional Zeta Values Bouillot, Olivier Mathematical Software – ICMS 2020 Article In this extended abstract, we present how to compute and visualize phase portraits of bi-dimensional Zeta Values. Such technology is useful to explore bi-dimensional Zeta Values and in long-term quest to discover a 2D-Riemann hypothesis. To reach this goal, we need two preliminary steps: [Formula: see text] the notion of phase portraits and a general tool to visualize phase portrait based on interactive Jupyter widgets. [Formula: see text] the ability to compute numerical approximations of bi-dimensional Zeta values, using mpmath, a Python library for arbitrary-precision floating-point arithmetic. To this end, we develop a theory to numerically compute double sums and produce the first algorithm to compute bi-dimensional Zeta Values with complex parameters. 2020-06-06 /pmc/articles/PMC7340897/ http://dx.doi.org/10.1007/978-3-030-52200-1_39 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Bouillot, Olivier
Phase Portraits of Bi-dimensional Zeta Values
title Phase Portraits of Bi-dimensional Zeta Values
title_full Phase Portraits of Bi-dimensional Zeta Values
title_fullStr Phase Portraits of Bi-dimensional Zeta Values
title_full_unstemmed Phase Portraits of Bi-dimensional Zeta Values
title_short Phase Portraits of Bi-dimensional Zeta Values
title_sort phase portraits of bi-dimensional zeta values
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340897/
http://dx.doi.org/10.1007/978-3-030-52200-1_39
work_keys_str_mv AT bouillotolivier phaseportraitsofbidimensionalzetavalues

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