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

Yuri Matiyasevich

doi:10.56994/JXM.001.002.003

paper

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

arXiv:2602.03408 · doi:10.56994/JXM.001.002.003

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.