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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
##### Keywords:
entire function; composition order; value distribution; order
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##### References:
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