An addition to the cos𝜋𝜌-theorem for subharmonic and entire functions of zero lower order

Chyzhykov, I.

doi:10.1090/S0002-9939-01-06188-3

An addition to the $\cos \pi \rho$-theorem for subharmonic and entire functions of zero lower order
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Proc. Amer. Math. Soc. 130 (2002), 517-528 Request permission

Abstract:

We obtain a sharp asymptotic relation between the infimum and the maximum on a circle of a subharmonic function of zero lower order. An example is constructed, which shows the sharpness of the relation in the class of entire functions of zero order such that $\log M(r,f)/\log ^2 r\to +\infty$, where $M(r,f)=\max \{|f(z)|: |z|=r\}$ as $r\to +\infty$.

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