Displaying similar documents to “Entire solutions of q-difference equations and value distribution of q-difference polynomials”

The zero distribution and uniqueness of difference-differential polynomials

Kai Liu, Xin-Ling Liu, Lian-Zhong Yang (2013)

Annales Polonici Mathematici

Similarity:

We consider the zero distribution of difference-differential polynomials of meromorphic functions and present some results which can be seen as the discrete analogues of the Hayman conjecture. In addition, we also investigate the uniqueness of difference-differential polynomials of entire functions sharing one common value. Our theorems improve some results of Luo and Lin [J. Math. Anal. Appl. 377 (2011), 441-449] and Liu, Liu and Cao [Appl. Math. J. Chinese Univ. 27 (2012), 94-104]. ...

Value distribution and uniqueness of difference polynomials and entire solutions of difference equations

Xiaoguang Qi (2011)

Annales Polonici Mathematici

Similarity:

This paper is devoted to value distribution and uniqueness problems for difference polynomials of entire functions such as fⁿ(f-1)f(z+c). We also consider sharing value problems for f(z) and its shifts f(z+c), and improve some recent results of Heittokangas et al. [J. Math. Anal. Appl. 355 (2009), 352-363]. Finally, we obtain some results on the existence of entire solutions of a difference equation of the form f ⁿ + P ( z ) ( Δ c f ) m = Q ( z ) .

Uniqueness theorems for entire functions whose difference polynomials share a meromorphic function of a smaller order

Xiao-Min Li, Wen-Li Li, Hong-Xun Yi, Zhi-Tao Wen (2011)

Annales Polonici Mathematici

Similarity:

We deal with uniqueness of entire functions whose difference polynomials share a nonzero polynomial CM, which corresponds to Theorem 2 of I. Laine and C. C. Yang [Proc. Japan Acad. Ser. A 83 (2007), 148-151] and Theorem 1.2 of K. Liu and L. Z. Yang [Arch. Math. 92 (2009), 270-278]. We also deal with uniqueness of entire functions whose difference polynomials share a meromorphic function of a smaller order, improving Theorem 5 of J. L. Zhang [J. Math. Anal. Appl. 367 (2010), 401-408],...

Difference of Function on Vector Space over F

Kenichi Arai, Ken Wakabayashi, Hiroyuki Okazaki (2014)

Formalized Mathematics

Similarity:

In [11], the definitions of forward difference, backward difference, and central difference as difference operations for functions on R were formalized. However, the definitions of forward difference, backward difference, and central difference for functions on vector spaces over F have not been formalized. In cryptology, these definitions are very important in evaluating the security of cryptographic systems [3], [10]. Differential cryptanalysis [4] that undertakes a general purpose...

Meromorphic solutions of q-shift difference equations

Kai Liu, Xiao-Guang Qi (2011)

Annales Polonici Mathematici

Similarity:

We establish a q-shift difference analogue of the logarithmic derivative lemma. We also investigate the value distributions of q-shift difference polynomials and the growth of solutions of complex q-shift difference equations.