Geodesic
Analogues of Wiman's theorem for Dirichlet series
Sbornik. Mathematics, Tome 38 (1981) no. 1, pp. 95-107 
M. N. Sheremeta. Analogues of Wiman's theorem for Dirichlet series. Sbornik. Mathematics, Tome 38 (1981) no. 1, pp. 95-107. http://geodesic.mathdoc.fr/item/SM_1981_38_1_a6/
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     title = {Analogues of {Wiman's} theorem for {Dirichlet} series},
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper studies the classes of integral functions $f$ that are given by a Dirichlet series which converges absolutely in the whole plane and has nonnegative indices and are such that $\ln M(x)\sim\ln\mu(x)$ as $x\to\infty$ outside some exceptional set, where $M(x)=\sup\{|f(x+iy)|:|y|<\infty\}$ and $\mu(x)$ is the maximum term in the Dirichlet series. Bibliography: 8 titles.

[1] A. Wiman, “Über den Zusammenhang zwischen dem Maximalbetrage einer analytischen Funktion und dem grossten Betrage bei gegebenem Argumente der Funktion”, Acta Math., 41 (1916), 1–28 | DOI | MR | Zbl

[2] K. Sugimura, “Übertragung einiger Satze aus der Theorie der ganzen Funktionen auf Dirichletschen Reihen”, Math. Z., 29 (1929), 264–277 | DOI | MR

[3] H. F. Yakunina, “K teoreme Vimana dlya ryadov Dirikhle”, Matem. analiz i ego prilozh., vyp. 4, Rostov-na-Donu, 1974, 218–225

[4] E. F. Schuchinskaya, Analogi teoremy Vimana dlya ryadov Dirikhle, Rostovsk. un-t, 1976; Рукопись деп. в ВИНИТИ 17 февр. 1977 г., No 651-77 Деп.

[5] M. N. Sheremeta, “Metod Vimana–Valirona dlya tselykh funktsii, zadannykh ryadami Dirikhle”, DAN SSSR, 238:6 (1978), 1307–1308 | MR

[6] M. N. Sheremeta, “Metod Vimana–Valirona dlya ryadov Dirikhle”, Ukr. matem. zh., 30:4 (1978), 488–497 | MR | Zbl

[7] M. A. Evgrafov, Asimptoticheskie otsenki i tselye funktsii, Fizmatgiz, Moskva, 1962 | MR

[8] B. Ya. Levin, Raspredelenie kornei tselykh funktsii, Gostekhizdat, Moskva, 1956