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Aspects of Zeta-Function Theory in the Mathematical Works of Adolf Hurwitz

In: From Arithmetic to Zeta-Functions

Author

Listed:
  • Nicola Oswald

    (University of Wuppertal, Department of Mathematics and Informatics)

  • Jörn Steuding

    (Universität Würzburg, Institut für Mathematik)

Abstract

Adolf Hurwitz is rather famous for his celebrated contributions to Riemann surfaces, modular forms, diophantine equations and approximation as well as to certain aspects of algebra. His early work on an important generalization of Dirichlet’s L-series, nowadays called Hurwitz zeta-function, is the only published work settled in the very active field of research around the Riemann zeta-function and its relatives. His mathematical diaries, however, provide another picture, namely a lifelong interest in the development of zeta-function theory. In this note we shall investigate his early work, its origin, and its reception, as well as Hurwitz’s further studies of the Riemann zeta-function and allied Dirichlet series from his diaries. It turns out that Hurwitz already in 1889 knew about the essential analytic properties of the Epstein zeta-function (including its functional equation) 13 years before Paul Epstein.

Suggested Citation

  • Nicola Oswald & Jörn Steuding, 2016. "Aspects of Zeta-Function Theory in the Mathematical Works of Adolf Hurwitz," Springer Books, in: Jürgen Sander & Jörn Steuding & Rasa Steuding (ed.), From Arithmetic to Zeta-Functions, pages 309-351, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-28203-9_20
    DOI: 10.1007/978-3-319-28203-9_20
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