Re: Question regarding natural logs

On 31-07-2007 17:19, Jay R. Yablon wrote:

I have been playing around a bit with natural logs in the course of some physics work, and have come across an interesting property of the ln function which is detailed in the file below:

http://jayryablon.files.wordpress.com/2007/07/natural-log.pdf

I would like to know if this a) is correct mathematically, b) if this has been notice before in this sort of form, and c) any references which this sort of "quantization" of an imaginary component of the natural log has been discussed. The ln is of course the inverse of exponentiation. Analogously to sin^-1 and cos^-1, it is, in its imaginary part, not a function but a multi-valued inverse.

This has been well-known since the 19th century, at least, and you will
find it on about *any* book ever written on Complex Analysis. But if you
want references, here they are: see Lang's Complex Analysis (chap. III,
section 6) or Remmert's Theory of Complex Functions (chap. 5, section
4).

Best regards,

Jose Carlos Santos
.