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Let $\zeta_{n}=e^{2\pi i /n}$ be the nth root of unity. Now consider the product : $$\prod_{k=1}^{n-1} (1-\zeta_{n}^{k})^{\zeta_{n}^{k}}$$ Is there a simple formula for this product as a function of $n$ !?

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    $\begingroup$ Note that $z^w$ is a multiple-valued function. Should we take the branch where $z$ doesn't lie on the negative real line? $\endgroup$ – Jonathan Y. Sep 6 '13 at 22:43
  • $\begingroup$ I'm afraid I don't take your meaning ! $\endgroup$ – Mohammad Al Jamal Sep 6 '13 at 22:52
  • $\begingroup$ Well, how do you define $(1-\zeta_n^k)^{\zeta_n^k}$? $\endgroup$ – Jonathan Y. Sep 6 '13 at 22:56
  • $\begingroup$ ah.. ok ... yes, your $z$ doesn't lie on the negative real line . $\endgroup$ – Mohammad Al Jamal Sep 6 '13 at 22:59

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