I am interested in knowing the origins of this useful result, but I haven't been able to precisely pinpoint the context of its first use. Most texts seem to indicate the result originally comes from Felix Klein, though the lemma is sometimes referred as Schottky's criterion. I would also like to know what the original formulation looks like, if anyone knows it.

Thank you so much for your help!

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    $\begingroup$ It would be a BigHelp(TM) if you explained what this is, and gave a link or two to a description of the derivation and practical applications (if any) $\endgroup$ – Carl Witthoft May 5 at 12:04
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    $\begingroup$ You might take a look at the wikipedia page on Schottky groups, if you wanted to explore this question further. The links at the bottom of that page contain lots of information, including the very last link which leads to some pages in the works of Fricke and Klein. $\endgroup$ – Lee Mosher May 5 at 12:53
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    $\begingroup$ Bleak et al. say that the first uses are Klein, Neue Beiträge zur Riemann'schen Functionentheorie (1883), III.16, and more expository Fricke-Klein, Vorlesungen über die Theorie der automorphen Functionen (1897), II.3.8. Both are freely accessible. The name is recent. $\endgroup$ – Conifold May 6 at 3:39
  • $\begingroup$ @CarlWitthoft You're completely right sorry. I previously asked this on MathSE and was told to post here, I should have given more context since this is not a math specific site. In any case Conifold's comment answers my question. $\endgroup$ – SFeesh May 7 at 18:15

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