In Search of Approximate Polynomial Dependencies Among the Derivatives of the Alternating Zeta Function

Authors

Yuri Matiyasevich Steklov Institute of Mathematics at St.Petersburg https://orcid.org/0000-0001-7046-3746

DOI:

https://doi.org/10.56994/JXM.001.002.003

Keywords:

Dirichlet eta function, Approximate polynomial relations among the derivatives

Abstract

It is well-known that the Riemann zeta function does not satisfy any exact polynomial differential equation. Here we present numerical evidence suggesting the existence of approximate polynomial dependencies between the values of the alternating zeta function and its initial derivatives.

A number of conjectures is stated.

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Published

08/30/2025

How to Cite

Matiyasevich, Y. (2025). In Search of Approximate Polynomial Dependencies Among the Derivatives of the Alternating Zeta Function. Journal of Experimental Mathematics, 1(2), 239–256. https://doi.org/10.56994/JXM.001.002.003

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Issue

Vol. 1 No. 2 (2025): Volume 1, Issue 2

Section

Articles

License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.