Geodesic
Dirichlet series with real coefficients that are unbounded
Sbornik. Mathematics, Tome 198 (2007) no. 6, pp. 793-815 Cet article a éte moissonné depuis la source Math-Net.Ru

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Entire Dirichlet series with real coefficients are studied in the case when the sequence of sign changes of the coefficients satisfies the Levinson condition. The best possible lower estimate for the growth rate of a Dirichlet series on the positive half-axis is obtained. Bibliography: 25 titles. 
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A. M. Gaisin. Dirichlet series with real coefficients that are unbounded. Sbornik. Mathematics, Tome 198 (2007) no. 6, pp. 793-815. http://geodesic.mathdoc.fr/item/SM_2007_198_6_a2/

[1] G. Pólya, “Untersuchungen über Lücken und Singularitäten von Potenzreihen”, Math. Z., 29:1 (1929), 549–640 | DOI | MR | Zbl

[2] M. N. Sheremeta, “Ob odnoi teoreme Poia”, Ukr. matem. zhurn., 35:1 (1983), 119–124 | MR | Zbl

[3] M. N. Sheremeta, “O tselykh funktsiyakh s veschestvennymi teilorovskimi koeffitsientami”, Ukr. matem. zhurn., 37:6 (1985), 786–787 | MR | Zbl

[4] A. M. Gaisin, “K odnoi teoreme Poia o tselykh funktsiyakh s veschestvennymi koeffitsientami Teilora”, Sib. matem. zhurn., 38:1 (1997), 46–55 | MR | Zbl

[5] A. I. Pavlov, “O roste na polozhitelnom luche tselykh funktsii s veschestvennymi koeffitsientami”, Matem. zametki, 14 (1973), 577–588 | MR | Zbl

[6] A. Edrei, “Gap and density theorems for entire functions”, Scripta Math., 23 (1957), 117–141 | MR | Zbl

[7] A. M. Gaisin, “Otsenka ryada Dirikhle s veschestvennymi koeffitsientami na luche”, Matem. zametki, 60:6 (1996), 810–823 | MR | Zbl

[8] M. N. Sheremeta, “Ob odnom svoistve tselykh funktsii s veschestvennymi teilorovskimi koeffitsientami”, Matem. zametki, 18:3 (1975), 395–402 | MR | Zbl

[9] A. M. Gaisin, “Reshenie problemy Poia”, Matem. sb., 193:6 (2002), 39–60 | MR | Zbl

[10] N. Levinson, Gap and density theorems, Amer. Math. Soc. Colloq. Publ., 26, Amer. Math. Soc., New York, 1940 | MR | Zbl

[11] Y. Domar, “On the existence of a largest subharmonic minorant of a given function”, Ark. Mat., 3:5 (1958), 429–440 | DOI | MR | Zbl

[12] E. M. Dynkin, “O roste analiticheskoi funktsii vblizi mnozhestva ee osobykh tochek”, Zapiski nauch. sem. LOMI, 30 (1972), 158–160 ; E. M. Dyn'kin, “Growth of an analytic function near its set of singular points”, J. Soviet Math., 4 (1975), 438–440 | MR | Zbl | DOI

[13] E. M. Dynkin, “Funktsii s zadannoi otsenkoi $\partial f/\partial\overline z$ i teorema N. Levinsona”, Matem. sb., 89(131):2(10) (1972), 182–190 | MR | Zbl

[14] A. L. Volberg, B. Erikke, “Summiruemost logarifma pochti analiticheskoi funktsii i obobschenie teoremy Levinsona–Kartrait”, Matem. sb., 130(172):3(7) (1986), 335–348 ; A. L. Vol'berg, B. Ërikke, “Summability of the logarithm of an almost analytic function and a generalization of the Levinson–Cartwright theorem”, Math. USSR-Sb., 58:2 (1987), 337–349 | MR | Zbl | DOI

[15] P. Koosis, The logarithmic integral., v. I, Cambridge Stud. Adv. Math., 12, Cambridge Univ. Press, Cambridge, 1988 | MR | Zbl

[16] A. M. Gaisin, I. D. Latypov, “Otsenka ryada Dirikhle s lakunami Feiera na veschestvennoi osi”, Sib. matem. zhurn., 45:1 (2004), 62–79 | MR | Zbl

[17] B. Berndtsson, “A note on Pavlov–Korevaar–Dixon interpolation”, Nederl. Akad. Wetensch. Indag. Math., 40:4 (1978), 409–414 | MR | Zbl

[18] A. M. Gaisin, “Otsenka ryada Dirikhle, pokazateli kotorogo – nuli tseloi funktsii s neregulyarnym povedeniem”, Matem. sb., 185:2 (1994), 33–56 ; A. M. Ga\u{i}sin, “An estimate for a Dirichlet series whose exponents are zeros of an entire function with irregular behavior”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 163–183 | MR | Zbl | DOI

[19] A. M. Gaisin, “Otsenka rosta i ubyvaniya tseloi funktsii beskonechnogo poryadka na krivykh”, Matem. sb., 194:8 (2003), 55–82 | MR | Zbl

[20] A. F. Leontev, Ryady eksponent, Nauka, M., 1976 | MR | Zbl

[21] V. S. Boichuk, “O nekotorykh svoistvakh utochnennogo poryadka”, Sib. matem. zhurn., 20:2 (1979), 229–236 | MR | Zbl

[22] A. M. Gaisin, “Usilennaya nepolnota sistemy eksponent i problema Makintaira”, Matem. sb., 182:7 (1991), 931–945 ; A. M. Gaisin, “Strong incompleteness of a system of exponentials, and Macintyre's problem”, Math. USSR-Sb., 73:2 (1992), 305–318 | MR | Zbl | DOI

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

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

[25] S. Mandelbroit, Kvazianaliticheskie klassy funktsii, ONTI, M., L., 1937