Phase portraits of bi-dimensional zeta values. (English) Zbl 1503.11115
Bigatti, Anna Maria (ed.) et al., Mathematical software – ICMS 2020. 7th international conference, Braunschweig, Germany, July 13–16, 2020. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12097, 393-405 (2020).
Summary: 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:
For the entire collection see [Zbl 1496.68012].
To reach this goal, we need two preliminary steps:
- ●
- the notion of phase portraits and a general tool to visualize phase portrait based on interactive Jupyter widgets.
- ●
- 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.
For the entire collection see [Zbl 1496.68012].
MSC:
| 11M06 | \(\zeta (s)\) and \(L(s, \chi)\) |
| 65D20 | Computation of special functions and constants, construction of tables |
References:
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