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

Erik Christian Hansen; Yonathan Stone; Jesse Wolfson

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

History and Overview 2022-11-07 v1 Classical Analysis and ODEs

Authors: Erik Christian Hansen , Yonathan Stone , Jesse Wolfson

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.

Keywords

dirichlet series algebraic differential equations ostrowski hilbert conjecture analytic functions translation

Cite

@article{arxiv.2211.02088,
  title  = {Alexander Ostrowski's "On Dirichlet Series and Algebraic Differential Equations"},
  author = {Erik Christian Hansen and Yonathan Stone and Jesse Wolfson},
  journal= {arXiv preprint arXiv:2211.02088},
  year   = {2022}
}

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50 pages. Comments welcome!

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

Abstract

Keywords

Cite

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