An estimate for a Dirichlet series whose exponents are zeros of an entire function with irregular behavior
Sbornik. Mathematics, Tome 81 (1995) no. 1, pp. 163-183 Cet article a éte moissonné depuis la source Math-Net.Ru

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Under sufficiently general assumptions an estimate is obtained of the sum of an entire Dirichlet series in terms of the maximum of its modulus on a vertical segment. An analogous estimate is obtained for the Dirichlet series converging only in a half-plane.
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A. M. Gaisin. An estimate for a Dirichlet series whose exponents are zeros of an entire function with irregular behavior. Sbornik. Mathematics, Tome 81 (1995) no. 1, pp. 163-183. http://geodesic.mathdoc.fr/item/SM_1995_81_1_a8/

[1] Binmore K. G., “A density theorem with an application to gap power series”, Trans. Amer. Math. Soc., 148:2 (1970), 367–384 | DOI | MR | Zbl

[2] Redheffer R. M., “Completeness of sets of complex exponentails”, Advances in Mathematics, 24 (1977), 1–62 | DOI | MR | Zbl

[3] Krasichkov-Ternovskii I. F., “Interpretatsiya teoremy Berlinga–Malyavena o radiuse polnoty”, Matem. sb., 180:3 (1989), 397–423 | MR

[4] Sheremeta M. N., “Rost v polose tselykh funktsii, predstavlennykh ryadami Dirikhle”, Izv. AN SSSR, 45:3 (1981), 674–687 | MR | Zbl

[5] Leontev A. F., Posledovatelnosti polinomov iz eksponent, Nauka, M., 1980 | MR

[6] Murai T., “The deficiency of entire functions”, Annales de l'Institut Fourier, 33:3 (1983), 39–58 | MR | Zbl

[7] Gaisin A. M., “Usilennaya nepolnota sistemy eksponent i problema Makintaira”, Matem. sb., 182:7 (1991), 931–945 | MR

[8] Berndtsson B., “A note on Pavlov–Korevaar–Dixon interpolation”, Nederl. Acad. Wet. Proc., 1978, no. A81, 400–414 | MR

[9] Gaisin A. M., “Asimptoticheskoe povedenie summy tselogo ryada Dirikhle na krivykh”, Issledovaniya po teorii priblizhenii, BNTs UrO AN SSSR, Ufa, 1989, 3–15 | MR | Zbl

[10] Goldberg A. A., Ostrovskii I. V., Raspredelenie znachenii meromorfnykh funktsii, Nauka, M., 1970 | MR