On~a~conjecture of Polya
Izvestiya. Mathematics , Tome 44 (1995) no. 2, pp. 281-299.

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For entire functions $F(z)$ of finite lower Ritt order, defined by Dirichlet series with positive exponents, a criterion is found for $$ \ln\sup\limits_{|t|\infty}\big|F(\sigma+it)\big|=[1+o(1)\ln\min\limits_{|t|\leqslant h}\big|F(\sigma+it)\big|\quad(0\infty) $$ to hold as $\sigma\to+\infty$ outside some exceptional set.
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A. M. Gaisin. On~a~conjecture of Polya. Izvestiya. Mathematics , Tome 44 (1995) no. 2, pp. 281-299. http://geodesic.mathdoc.fr/item/IM2_1995_44_2_a3/

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