Chang Huang

Exact Angular Critical-Point Counts for e^z ± 1

For f_a(z) = e^z + a, a = ±1, we count the distinct angular critical points of log |f_a| on every zero-free circle of radius r ≥ 12. Writing N_p(r) for the number of zeros in the disk, we prove that the critical-point count N_osc(r) satisfies 0 ≤ N_osc(r) − 2N_p(r) ≤ 4, with both...