Value Distribution and Uniqueness Results of Zero-Order Meromorphic Functions to Their q-Shift
We investigate value distribution and uniqueness problems of meromorphic functions with their q-shift. We obtain that if f is a transcendental meromorphic (or entire) function of zero order, and Q(z) is a polynomial, then afn(qz)+f(z)−Q(z) has infinitely many zeros, where q∈ℂ∖{0}, a is nonzero const...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/818052 |
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| Summary: | We investigate value distribution and uniqueness problems of meromorphic functions with their q-shift. We obtain that if f is a transcendental meromorphic (or entire) function of zero order, and Q(z) is a polynomial, then afn(qz)+f(z)−Q(z) has infinitely many zeros, where q∈ℂ∖{0}, a is nonzero constant, and n≥5 (or n≥3). We also obtain that zero-order meromorphic function share is three distinct values IM with its q-difference polynomial P(f), and if limsup r→∞(N(r,f)/T(r,f))<1, then f≡P(f). |
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| ISSN: | 1026-0226 1607-887X |