Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지

ON THE SIZE OF THE SET WHERE A MEROMORPHIC FUNCTION IS LARGE

  • Kwon, Ki-Ho (Department of Mathematics Korea Military Academy)
  • Received : 2010.11.16
  • Accepted : 2010.12.11
  • Published : 2010.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we investigate the extent of the set on which the modulus of a meromorphic function is lower bounded by a term related to some Nevanlinna Theory functionals. A. I. Shcherba estimate the size of the set on which the modulus of an entire function is lower bounded by 1. Our theorem in this paper shows that the same result holds in the case that the lower bound is replaced by$lT(r,f)$, $0{\leq}l$ < 1, which improves Shcherba's result. We also give a similar estimation for meromorphic functions.

Keywords

References

  1. J. M. Anderson and A. Baernstein II, The size of the set on which a meromorphic function is large, Proc. Lond. Math. Soc., 36(3)(1978), 518-539. https://doi.org/10.1112/plms/s3-36.3.518
  2. K. Arima, On maximum modulus of integral functions, J. Math. Soc. Japan, 4(1952), 62-66. https://doi.org/10.2969/jmsj/00410062
  3. A. Baernstein, Proof of Edrei's conjecture, Proc. Lond. Math. Soc., 25(3)(1973), 418-434.
  4. A. Edrei, Sums of deficiencies of meromorphic functions, J. Anal. Math., 14(1965) 79-107. https://doi.org/10.1007/BF02806380
  5. A.A. Gol'dberg, On the relationship between a defect and a deviations of a meromorphic function, Teoriya Funktsii, Funkts. Analiz I Ikh Prilozh., 29(1978), 31-35.
  6. W. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964.
  7. K. Kwon, On the growth of entire functions, Israel J. Math., 86(1994), 409-427. https://doi.org/10.1007/BF02773689
  8. A.I. Shcherba, On a set on which an entire function is lower bounded, Russian Math. Izvestiya VUZ. Matematika, 34(9)(1990), 75-81.