Zech's logarithms are defined in here.

I couldn't find a reason why they are called "Zech". The only thing a dictionary suggests is that Zech is an abbreviation for Zechariah, which doesn't seem relevant, right?!

So, could you please shed light on this naming?

  • $\begingroup$ From the "'s" part, I'd guess they were invented or studied in detail by some person whose last name was "Zech" $\endgroup$ – celtschk Jul 13 '13 at 21:57
  • $\begingroup$ @celtschk: Thanks. But who was he? Wikipedia mentions that they were studied by "Jacobi", whose full name is "Carl Gustav Jacob Jacobi". So, who's Zech? $\endgroup$ – M.S. Dousti Jul 13 '13 at 21:59
  • 2
    $\begingroup$ The only mathematician with that name I could find is Julius August Christoph Zech (1821–1864). Unfortunately the internet doesn't seem to have any more information about him. The dates and the fact that he was mathemnatician and astronomers are all I could find (he's listed in the German Wikipedia page for the name Zech, but unfortunately there's no dedicated Wikipedia page about him). Is is of course possible that this is just a name coincidence. $\endgroup$ – celtschk Jul 13 '13 at 22:05
  • $\begingroup$ @celtschk: Great find, thanks! $\endgroup$ – M.S. Dousti Jul 13 '13 at 22:11


The reason for the name is that Julius Zech (1849) published a table of these logarithms (which he called 'addition logarithms') for doing arithmetic in $\mathbb{Z}$/p. These were, I think, intended for number-theoretical calculations.

From Oliver Pretzel - "Error-correcting codes and finite fields".

Edit: Gerhard Betsch up at "Math Forum" has written up a piece about his personal history and research. Among other things, he writes:

... Zech's tables were designed as a tool for calculations in theoretical astronomy. The preface makes no reference to Jacobi, and of course no reference to finite fields.

  • $\begingroup$ Julius August Christoph Zech, 1821–1864, German mathematician and astronomer. His vita is missing completely from English Wikipedia and only exists as a redlink under the family name Zech in German Wikipedia ... $\endgroup$ – Hagen von Eitzen Jul 13 '13 at 22:46

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