The size of the set on which an entire function is large

Abstract

We consider the relationship between the number of separated maximum modulus points of an entire function and the Lebesgue measure of the set \\alpha \\log {M(r,f)}}\\} $ ]]> { θ : log ⁡ | f ( r e iθ ) | > αlog ⁡ M ( r , f ) } ( 0 ≤ α < 1 ) . The results of Arima and Baernstein are generalized. We also give examples showing that the obtained estimate is sharp.