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 Izv. Akad. Nauk SSSR Ser. Mat., 1969, Volume 33, Issue 2, Pages 414–454 (Mi izv2136)

This article is cited in 16 scientific papers (total in 16 papers)

Growth of meromorphic functions of finite lower order

V. P. Petrenko

Abstract: A new measure $\beta(a,f)$ of the deviation of a meromorphic function from a number $a$ is introduced in order to study the deeper asymptotic properties of meromorphic functions. It is found that $\beta(a,f)$ possesses many properties analogous to those of the deficiencies introduced by R. Nevanlinna.

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English version:
Mathematics of the USSR-Izvestiya, 1969, 33:2, 391–432

Bibliographic databases:

UDC: 517.5
MSC: 30D30, 30D15, 32A22, 33E12
Received: 12.05.1968

Citation: V. P. Petrenko, “Growth of meromorphic functions of finite lower order”, Izv. Akad. Nauk SSSR Ser. Mat., 33:2 (1969), 414–454; Math. USSR-Izv., 33:2 (1969), 391–432

Citation in format AMSBIB
\Bibitem{Pet69} \by V.~P.~Petrenko \paper Growth of meromorphic functions of finite lower order \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1969 \vol 33 \issue 2 \pages 414--454 \mathnet{http://mi.mathnet.ru/izv2136} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=251226} \zmath{https://zbmath.org/?q=an:0194.11101} \transl \jour Math. USSR-Izv. \yr 1969 \vol 33 \issue 2 \pages 391--432 \crossref{https://doi.org/10.1070/IM1969v003n02ABEH000786} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. P. Petrenko, “The study of the structure of the set of positive deviations of meromorphic functions. I”, Math. USSR-Izv., 3:6 (1969), 1251–1270
2. V. P. Petrenko, “A study of the structure of the set of positive deviations of meromorphic functions. II”, Math. USSR-Izv., 4:1 (1970), 31–57
3. V. K. Fedyanin, “On the critical indices in the ising model”, Theoret. and Math. Phys., 7:2 (1971), 504–510
4. V. P. Petrenko, M. Khussain, “On the growth of entire curves”, Math. USSR-Izv., 7:2 (1973), 467–478
5. T. B. Lamzina, “On the magnitudes of the deviations of entire curves of lower order $\lambda<1$”, Math. USSR-Izv., 8:2 (1974), 328–338
6. V. P. Petrenko, “The growth of integral curves of finite lower order”, Math. USSR-Sb., 26:4 (1975), 427–448
7. V. P. Petrenko, “On the connection between the deviation values and the Valiron defects for integral curves and variable polyvectors”, Math. USSR-Izv., 10:2 (1976), 309–319
8. V. P. Petrenko, “Growth of entire functions of two complex variables that are slowly increasing in one of the variables”, Math. USSR-Izv., 10:1 (1976), 63–92
9. V. I. Krutin', “On the magnitudes of the positive deviations and of the defects of entire curves of finite lower order”, Math. USSR-Izv., 13:2 (1979), 307–334
10. G. A. Barsegyan, “On the geometry of meromorphic functions”, Math. USSR-Sb., 42:2 (1982), 155–196
11. B. N. Khabibullin, “On the type of entire and meromorphic functions”, Russian Acad. Sci. Sb. Math., 77:2 (1994), 293–301
12. B. N. Khabibullin, “The theorem on the least majorant and its applications. II. Entire and meromorphic functions of finite order”, Russian Acad. Sci. Izv. Math., 42:3 (1994), 479–500
13. Walter Bergweiler, Heinrich Bock, “On the growth of meromorphic functions of infinite order”, J Anal Math, 64:1 (1994), 327
14. B. N. Khabibullin, “Paley problem for plurisubharmonic functions of finite lower order”, Sb. Math., 190:2 (1999), 309–321
15. I. I. Marchenko, “On upper and lower bounds for logarithmic densities in the theory of meromorphic functions”, Russian Math. (Iz. VUZ), 46:10 (2002), 62–68
16. L. V. Kaluzhynova, I. I. Marchenko, “On the Magnitudes of Deviations of Entire Functions of Infinite Order from Rational Functions”, Math. Notes, 85:1 (2009), 20–33
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