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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  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath
    3. V. K. Fedyanin, “On the critical indices in the ising model”, Theoret. and Math. Phys., 7:2 (1971), 504–510  mathnet  crossref
    4. V. P. Petrenko, M. Khussain, “On the growth of entire curves”, Math. USSR-Izv., 7:2 (1973), 467–478  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath
    6. V. P. Petrenko, “The growth of integral curves of finite lower order”, Math. USSR-Sb., 26:4 (1975), 427–448  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath  isi
    10. G. A. Barsegyan, “On the geometry of meromorphic functions”, Math. USSR-Sb., 42:2 (1982), 155–196  mathnet  crossref  mathscinet  zmath
    11. B. N. Khabibullin, “On the type of entire and meromorphic functions”, Russian Acad. Sci. Sb. Math., 77:2 (1994), 293–301  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. Walter Bergweiler, Heinrich Bock, “On the growth of meromorphic functions of infinite order”, J Anal Math, 64:1 (1994), 327  crossref  mathscinet  zmath
    14. B. N. Khabibullin, “Paley problem for plurisubharmonic functions of finite lower order”, Sb. Math., 190:2 (1999), 309–321  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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  mathnet  mathscinet  zmath  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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