On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane

Chiang, Yik-Man; Song, Feng

doi:10.1007/s11139-007-9101-1

Cited by 603 publications

(379 citation statements)

References 33 publications

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“…Recently, the difference variant of Nevanlinna theory has been established independently in [2,6,7,8]. With the development of difference analogue of Nevanlinna theory, many authors paid their attentions to the difference version of Hayman conjecture.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

VALUE DISTRIBUTION OF SOME q-DIFFERENCE POLYNOMIALS

Xu¹,

Zhong²

2016

Bulletin of the Korean Mathematical Society

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Section: Introduction and Main Resultsmentioning

confidence: 99%

VALUE DISTRIBUTION OF SOME q-DIFFERENCE POLYNOMIALS

Xu¹,

Zhong²

2016

Bulletin of the Korean Mathematical Society

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“…For a ∈ C = C ∪ {∞}, the deficiency of a with respect to a meromorphic function f is defined as Recently, the difference counterparts of Nevanlinna theory have been established. The key result is the difference analogue of the lemma on the logarithmic derivative obtained by Halburd-Korhonen [10] and Chiang-Feng [6], independently. Subsequently Halburd and Korhonen [11] showed how all key results of the Nevanlinna theory have corresponding difference variants as well.…”

Section: Definition 12 ([12]mentioning

confidence: 92%

Study of solutions of logarithmic order to higher order linear differential-difference equations with coeffcients having the same logarithmic order

Belaïdi¹

2017

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Abstract. The main purpose of this paper is to study the growth of solutions of the linear differential-difference equationwhere Aij(z) (i = 0, · · · , n; j = 0, · · · , m) are entire or meromorphic functions of finite logarithmic order and ci (0, · · · , n) are distinct complex numbers. We extend some precedent results due to Wu and Zheng and others.1. Introduction and main results. Throughout this paper, we assume that readers are familiar with the standard notations and the fundamental results of the Nevanlinna value distribution theory of meromorphic functions ([12, 19]). Let f be a meromorphic function; we define m(r, f ) = 1 2πand T (r, f ) = m(r, f ) + N (r, f ) (r > 0)2010 Mathematics Subject Classification. 30D35, 34K06, 34K12.

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“…Lemma 2.4 (see [5]). Let f (z) be a transcendental meromorphic function with finite order σ and η be a nonzero complex number.…”

Section: Some Lemmasmentioning

confidence: 99%

Shared Values and Borel Exceptional Values for High Order Difference Operators

Liao¹,

Zhang²

2016

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, we investigate the high order difference counterpart of Brück's conjecture, and we prove one result that for a transcendental entire function f of finite order, which has a Borel exceptional function a whose order is less than one, if ∆ n f and f share one small function d other than a CM, then f must be form of f (z) = a + ce βz , where c and β are two nonzero constants such that d−∆ n a d−a = (e β − 1) n . This result extends Chen's result from the case of σ(d) < 1 to the general case of σ(d) < σ(f ).

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On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane

Cited by 603 publications

References 33 publications

VALUE DISTRIBUTION OF SOME q-DIFFERENCE POLYNOMIALS

VALUE DISTRIBUTION OF SOME q-DIFFERENCE POLYNOMIALS

Study of solutions of logarithmic order to higher order linear differential-difference equations with coeffcients having the same logarithmic order

Shared Values and Borel Exceptional Values for High Order Difference Operators

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