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Does anyone know where to find an English translation of Riemann's Habilitation Thesis concerning trigonometric series? The German title of the work is "Über die Darstellbarkeit einer Function durch eine trigonometrische Reihe" and the English title is "On the representation of a function as a Trigonometric Series". So far I unfortunately haven't been able to find the English translation, so any suggestions as to where I might find it (if it has been translated) would be greatly appreciated.

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3 Answers 3

up vote 3 down vote accepted

This is XII in Riemann's Werke (1876; 1892) and has been published in English in

Bernhard Riemann, Collected papers. Translated from the 1892 German edition by Roger Baker, Charles Christenson and Henry Orde. Kendrick Press, Heber City, UT, 2004 ISBN: 0-9740427-2-2; 0-9740427-3-0 MR2121437 (2005m:01028)

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Thanks very much! –  Lea M Jul 2 '10 at 21:29

After some googling, I couldn't find an English translation, but I found (cf Chapter 38 of "Landmark writings in Western mathematics 1640-1940" (eds. Grattan-Guinness, Cook)) a reference to a French translation:

Bulletin des sciences math\'ematiques, (1) 5 (1873), 20-48, 79-96

Reprinted in Riemann's Oeuvres math\'ematiques (ed. Laugel), Paris: Gauthier-Villars, 1898, 227-279.

(Also that chapter 38 I mentioned seems to have a detailed explanation, in English, of the contents of the paper.)

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Thanks very much! –  Lea M Jul 2 '10 at 21:30

Riemann's complete papers, including are available used on amazon, currently for $80. Search for ISBN-10: 0974042730.

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