Abstract
Letf(z) be meromorphic function of finite nonzero orderρ. Assuming certain growth estimates onf by comparing it withr ρ L(r) whereL(r) is a slowly changing function we have obtained the bounds for the zeros off(z) −g (z) whereg (z) is a meromorphic function satisfyingT (r, g)=o {T(r, f)} asr → ∞. These bounds are satisfied but for some exceptional functions. Examples are given to show that such exceptional functions exist.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hardy, G. H. and Rogosinski, W. W. “Notes on Fourier Series. III. Asymptotic formulae for certain trigonometrical series,”Quarterly Journal of Mathematics, Oxford Series, 1945,16, 49–58.
Hayman, W. K. ..Meromorphic Functions, Oxford, 1964.
Levin, B. Ja. ..Distribution of Zeros of Entire Functions, 1964, Vol. 5, (A.M.S.),
Nevanlinna, R. .. Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Paris, 1929.
Shah, S. M... “Exceptional values of entire and meromorphic functions,”Journal Ind. Math. Soc., 1956,20, 315–17.
—————.. “Meromorphic functions of finite order,”Proc. Am. Math. Soc., 1959,10, 810–21.
Singh, S. K... “Exceptional values of entire functions,”Duke Math. Journal, 1956,24, 527–32.
Author information
Authors and Affiliations
Additional information
Communicated by Prof. B. S. Madhava Rao,f.a.sc.
Rights and permissions
About this article
Cite this article
Narayanan, K.A. On exceptional values of entire and meromorphic functions. Proc. Indian Acad. Sci. 80, 75–84 (1974). https://doi.org/10.1007/BF03046683
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF03046683