Let $z_j$ ($j=1,\dots, k$) be $k$ points on the complex plane none of which lies on the real line. Is it always true that the function $$ F(x)=\sum_{j=1}^k \frac{1}{|x-z_j|^2} $$ has at most $k$ local maxima on the real line?
Number of local maxima of a function
26
$\begingroup$
real-analysis
complex-analysis
analysis