Jensen zero-count bound ($n_f(r)\log (R/r)\le \log M_f(R)-\log |f(0)|$)

Every zero in the smaller disk contributes at least $\log (R/r)$ in Jensen's formula. Bounding the outer circle average by its maximum proves the estimate. With $R=2r$, an exponential $O(r\log r)$ maximum bound gives an $O(r\log r)$ zero count.