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In two papers from 1848 and 1850, the Russian mathematician Pafnuty L'vovich Chebyshev attempted to prove the asymptotic law of distribution of prime numbers. His work is notable for the use of the zeta function ζ(s) predating Riemann's celebrated memoir of 1859 - wikipedia

I could not find these two papers, I think they may not have been translated to English. Oeuvres de P.L. Tchebychef is available on archive but I checked the table of contents and I don't think it covers this work.

Where can I read about his use of zeta functions and original proof?

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2 Answers 2

up vote 5 down vote accepted

A source book in mathematics (David Eugene Smith) has a translation by Tamarkin of relevant work. The book can be seen through Google Books. There is not enough space in this answer for the url.

There is indeed use of the zeta-function in the paper, but it is the real zeta-function, which goes back to Euler.

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Wonderful! archive.org/details/sourcebookinmath00smit –  quanta May 10 '11 at 14:48
    
@quanta: Mine was books.google.ca/… –  André Nicolas May 10 '11 at 14:57
    
Although the above book omits the majority of Chebychev's paper it is still useful. –  quanta May 10 '11 at 15:09
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"There is not enough space in this answer for the url." - A Google Books tip: only the id= and pg= portions have to be retained for compact addresses, like so: books.google.com/books?id=awAfO7Ff_z0C&pg=PA127 –  J. M. May 10 '11 at 15:20
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@quanta: I think most of the papers are available online (in French). For example, see www-mathdoc.ujf-grenoble.fr/JMPA/PDF/JMPA_1852_1_17_A19_0.pdf –  André Nicolas May 10 '11 at 15:36

In the dover book Riemann's zeta function HM Edwards mentions that his papers are only in French an Russian. He also presents a few proofs from the papers that may be of interest to you. P. 281 Of course this book is from 1974... so maybe a translation has happened since.

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