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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 \[ \limsup_{r \to\infty} {\overline N\bigl( r,0;f(g)-Q\bigr) \over T(r,g)}=\infty. \]

MSC:
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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