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Alexander Ostrowski's "On Dirichlet Series and Algebraic Differential Equations"

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arxiv 2211.02088 v1 pith:X7GWBTXE submitted 2022-11-03 math.HO math.CA

Erik Christian Hansen , Yonathan Stone , Jesse Wolfson This is my paper · ORCID
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abstract

This is an English translation of Ostrowski's article "\"Uber Dirichletsche Reihen und algebraische Differentialgleichungen" published German in Math. Zeit. vol. 8, 1920, pp. 241-298. In this article, Ostrowski proves a conjecture of Hilbert that the two variable function $\zeta(x,s)=\sum_{n\ge 1} \frac{x^n}{n^s}$ cannot be written as a composition of analytic functions of one variable and algebraic functions of any number of variables.

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  1. Discovering Polynomial and Quadratic Structure in Nonlinear Ordinary Differential Equations

    cs.SC 2025-02 conditional novelty 3.0 of 10

    A survey of polynomialization and quadratization of ODEs, covering existence theorems, algorithms, software tools, and worked examples from neural networks and cell signaling.

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