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

Year: 2025

Type: article

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.

Source: Journal of Experimental Mathematics

DOI: 10.56994/jxm.001.002.003

Author: Yuri Matiyasevich

Institutions: St. Petersburg Department of Steklov Institute of Mathematics, Steklov Mathematical Institute

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W4413853948

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