Geodesic
The growth of integral curves of finite lower order
Sbornik. Mathematics, Tome 26 (1975) no. 4, pp. 427-448 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is concerned with the study of the deviations of integral curves of finite lower order. The basic result is that if a $p$-dimensional integral curve $\mathbf G(z)$ has finite lower order $\lambda,$ then its deviations with respect to an arbitrary fixed admissible system of vectors $A$ satisfy $$ \sum_{a\in A}\beta(a,\mathbf G)\leqslant K(1+\lambda)(p!)^3, $$ where $K$ is an absolute constant. This estimate is an analogue of the classical relation for the defects of integral curves. Bibliography: 31 titles. 
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     title = {The growth of integral curves of finite lower order},
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     volume = {26},
     number = {4},
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     url = {http://geodesic.mathdoc.fr/item/SM_1975_26_4_a0/}
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V. P. Petrenko. The growth of integral curves of finite lower order. Sbornik. Mathematics, Tome 26 (1975) no. 4, pp. 427-448. http://geodesic.mathdoc.fr/item/SM_1975_26_4_a0/

[1] R. Nevanlinna, Odnoznachnye analiticheskie funktsii, Gostekhizdat, Moskva, Leningrad, 1941

[2] V. P. Petrenko, “Rost meromorfnykh funktsii konechnogo nizhnego poryadka”, DAN SSSR, 184:5 (1969), 1031–1033 | MR | Zbl

[3] V. P. Petrenko, “Rost meromorfnykh funktsii konechnogo nizhnego poryadka”, Izv. AN SSSR, seriya matem., 33 (1969), 414–454 | MR | Zbl

[4] V. P. Petrenko, “Izuchenie struktury mnozhestva polozhitelnykh otklonenii meromorfnykh funktsii, I”, Izv. AN SSSR, seriya matem., 33 (1969), 1330–1348 | MR

[5] V. P. Petrenko, “Izuchenie struktury mnozhestva polozhitelnykh otklonenii meromorfnykh funktsii, II”, Izv. AN SSSR, seriya matem., 34 (1970), 32–56 | MR

[6] V. P. Petrenko, “O strukture mnozhestva polozhitelnykh otklonenii meromorfnykh funktsii”, DAN SSSR, 189:4 (1969), 718–720 | MR | Zbl

[7] V. P. Petrenko, “O velichinakh otklonenii tselykh krivykh nizhnego poryadka $\lambda1$”, DAN SSSR, 207:3 (1972), 538–540 | MR | Zbl

[8] I. P. Proskurnya, “O roste meromorfnykh funktsii beskonechnogo nizhnego poryadka”, DAN SSSR, 209:3 (1973), 558–561 | Zbl

[9] T. B. Lamzina, “O roste meromorfnykh funktsii i tselykh krivykh”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, no. 18, Kharkov, 1973, 202–215 | MR | Zbl

[10] N. V. Govorov, “O gipoteze Peili”, Funkts. analiz, 3:2 (1969), 41–45 | MR | Zbl

[11] H. Weyl, Meromorphic functions and analytic curves, Princeton, 1943 | MR

[12] L. Ahlfors, “The theory of meromorphic curves”, Acta Soc. Sci. Fenn., 3:4 (1941), 1–31 | MR

[13] H. Cartan, “Sur les zeros des combinaisons lineaires de $p$ fonctions holomorphes donnees”, Mathematica, 7 (1933), 5–31 | Zbl

[14] A. A. Goldberg, Dopolnenie k kn.: G. Vittikh, Noveishie issledovaniya po odnoznachnym analiticheskim funktsiyam, Fizmatgiz, M., 1960 | MR

[15] V. P. Petrenko, M. Khussain, “O roste tselykh krivykh”, Izv. AN SSSR, seriya matem., 37 (1973), 466–477 | MR | Zbl

[16] M. Khussain, “O defektakh i velichinakh otklonenii tselykh krivykh”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, no. 20, Kharkov, 1974

[17] W. H. J. Fuchs, “Theorem on the Nevanlinna's deficiencies of meromorphic functions of finite order”, Ann. Math., 68:2 (1958), 203–209 | DOI | MR | Zbl

[18] V. P. Petrenko, “O roste $Q$-psevdomeromorfnykh funktsii”, DAN SSSR, 196:1 (1971), 50–52 | MR | Zbl

[19] V. P. Petrenko, “O velichinakh otklonenii i defektakh $Q$PM-funktsii”, Sib. matem. zh., 13:4 (1972), 823–840 | MR | Zbl

[20] V. P. Petrenko, “Rost $Q$-psevdomeromorfnykh funktsii”, Sib. matem. zh., 15:1 (1974), 76–89 | MR | Zbl

[21] V. K. Khaiman, Meromorfnye funktsii, Mir, M., 1966 | MR

[22] B. Ya. Levin, Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956

[23] R. Nevanlinna, Le theoreme de Picard–Borel et la theorie des fonctions meromorphes, Paris, 1929

[24] V. P. Petrenko, “Nekotorye otsenki dlya velichin defektov meromorfnykh funktsii”, Sib. matem. zh., 7:6 (1966), 1319–1336 | MR | Zbl

[25] V. P. Petrenko, “O roste meromorfnykh funktsii konechnogo nizhnego poryadka i velichinakh ikh defektov”, Sib. matem. zh., 8:5 (1967), 1156–1189 | MR | Zbl

[26] A. Weitsman, “A theorem on Nevanlinna deficiencies”, Acta Math., 128:1,2 (1972), 41–52 | DOI | MR | Zbl

[27] V. P. Petrenko, “O velichinakh defektov meromorfnykh funktsii”, DAN SSSR, 158:5 (1964), 1030–1033 | MR | Zbl

[28] V. P. Petrenko, “Nekotorye otsenki logarifmicheskoi proizvodnoi meromorfnoi funktsii”, Izv. AN Arm.SSR, 17:1 (1964), 23–37 | MR | Zbl

[29] S. Saks, Teoriya integrala, IL, M., 1949

[30] N. Petridis, “Sur les transformations interieures et les courbes pseudomeromorphes”, C. R. Acad. Sci., 261:7 (1965), 1581–1584 | MR | Zbl

[31] X. By, Teoriya ravnoraspredeleniya dlya golomorfnykh krivykh, Mir, M., 1973 | MR