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

TL;DR

This paper provides numerical evidence suggesting the existence of approximate polynomial relationships between the alternating zeta function and its derivatives, proposing new conjectures about these dependencies.

Contribution

It introduces the idea of approximate polynomial dependencies among derivatives of the alternating zeta function and formulates related conjectures.

Findings

Numerical evidence for approximate polynomial dependencies

Formulation of new conjectures about these dependencies

Insights into the behavior of the alternating zeta function derivatives

Abstract

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