Talk:Cohn's theorem

Missing complex conjugate sign in the conjugate reciprocal formula
If $f(z) = a_{0} + &hellip; + a_{n}z^{n}$ is a polynomial, then its conjugate reciprocal is given by reversing and conjugating the coefficients, i.e., $f^{*}(z) = \overline{a_{n}} + &hellip; + \overline{a_{0}}z^{n}|undefined$.

The formula for conjugate reciprocal (when $z&ne;0$) should be $f^{*}(z) = z^{n} f(1/\overline{z})$, i.e., there should be a complex conjugate sign on both the input and output of $f$.

Steps:



The article was missing a complex conjugate on the input of $f(z) = a_{0} + &hellip; + a_{n}z^{n}$, so I added it in. This matches the formula used in the Lehmer–Schur algorithm article.

Arthur Cohn made the same mistake all throughout his 1921 PhD dissertation 😄. [1] (See e.g. equation (1) on page 112.)

[1] https://gdz.sub.uni-goettingen.de/id/PPN314393552

X-Fi6 (talk) 01:45, 4 December 2022 (UTC)