zbMATH — the first resource for mathematics

Entire functions that share one value with their linear differential polynomials. (English) Zbl 0985.30019
Suppose that \(f,g\) are two transcendental entire functions and \(Q\) is an entire function with \(T(r,Q)=O (T(r,g))\). If (i) the order \(\rho(f)\) of \(f\) is smaller than \(1/2\) or an irrational number, (ii) the lower order \(\lambda (g)\) of \(g\) is finite, then the exponent of convergence of the zeros of \(f(z)-Q\) is infinite or \[ \limsup_{r \to\infty} {\overline N\bigl( r,0;f(g)-Q\bigr) \over T(r,g)}=\infty. \]

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
Full Text: DOI
[1] J. CLUNIE, On integral and meromorphic functions, J. London Math. Soc, 37 (1962), 17-27. · Zbl 0104.29504 · doi:10.1112/jlms/s1-37.1.17
[2] W. DOERINGER, Exceptional values of differential polynomial, Pacific J. Math., 98 (1982), 55 62. · Zbl 0445.30025 · doi:10.2140/pjm.1982.98.55
[3] G. G. GUNDERSEN, Meromorphic functions that share finite values with their derivative, J. Math. Anal. Appl., 75 (1980), 441-446 · Zbl 0447.30018 · doi:10.1016/0022-247X(80)90092-X
[4] W. K. HAYMAN, Meromorphic Functions, Clarendon Press, Oxford, 1964 · Zbl 0115.06203
[5] G. JANK, E. MUES AND L. VOLKMANN, Meromorphe funktionen, die mit iher ersten un Zweiten Ableitung einen endlichen Wert teilen, Complex Variables Theory Appl., 6 (1986), 51-71. · Zbl 0603.30037
[6] I. LAINE, Nevanlinna Theory and Complex Differential Equations, Water de Gruyter, Ne York, 1993. · Zbl 0784.30002
[7] E. MUES AND N. STEINMETZ, Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen, Manuscpta Math., 29 (1979), 195-206 · Zbl 0416.30028 · doi:10.1007/BF01303627 · eudml:154660
[8] L. A. RUBEL AND C. C. YANG, Values shared by an entire function and its derivative, Lectur Notes m Math., 599, Sprmger-Verlag, Berlin, 1977, 101-103. · Zbl 0362.30026
[9] L. Z. YANG, Entire functions that share one value with their derivatives, Bull. Hong Kon Math. Soc, 2 (1998), 115-121. · Zbl 0926.30020
[10] H. ZHONG, Entire functions that share one value with their derivatives, Kodai Math. J., 1 (1995), 250-259. · Zbl 0840.30013 · doi:10.2996/kmj/1138043421
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.