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Article ID: CBB449429999

On a Relation Between Modular Functions and Dirichlet Series: Found in the Estate of Adolf Hurwitz (2017)

Oswald, Nicola M. R. (Author)

Archive for History of Exact Sciences
Volume: 71
Issue: 4
Pages: 345-361

DOI: 10.1007/s00407-017-0190-y

URI: https://link.springer.com/article/10.1007/s00407-017-0190-y

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Adolf Hurwitz’s estate contains a note from the early 1880s on the converse to Riemann’s proof of the functional equation for the zeta-function; this idea has later been elaborated by Hans Hamburger for a characterization of the zeta-function by its functional equation and by Eugène Cahen and Erich Hecke with respect to modular forms. In this note, we present Hurwitz’s reasoning and comment on the historical context.

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