$\cos \pi \lambda$ again

Abstract:

It is shown that if, for an entire function, \[ \liminf _{r\to \infty } \log M(r)/r^{\lambda } = 0 \] where $0< \lambda <1$, then \[ \limsup _{r\to \infty }(\log m(r)-\cos \pi \lambda \log M(r))/\log r = \infty . \] In the proof, the zeros of the function are redistributed to minimize the large values of $\log m(r) -\cos \pi \lambda \log M(r)$.