GENERALIZED YANG'S CONJECTURE ON THE PERIODICITY OF ENTIRE FUNCTIONS

被引：17

作者：

Liu, Kai ^{[1
]}

Wei, Yuming ^{[1
]}

Yu, Peiyong ^{[1
]}

机构：

[1] Nanchang Univ, Dept Math, Nanchang 330031, Jiangxi, Peoples R China

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2020年 / 57卷 / 05期

关键词：

Entire functions; periodicity; differential-difference equations; DIFFERENTIAL-DIFFERENCE EQUATIONS;

D O I：

10.4134/BKMS.b190934

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

On the periodicity of transcendental entire functions, Yang's Conjecture is proposed in [6, 13]. In the paper, we mainly consider and obtain partial results on a general version of Yang's Conjecture, namely, if f(z)(n) f((k))(z) is a periodic function, then f (z) is also a periodic function. We also prove that if f (z)(n) + f((k)) (z) is a periodic function with additional assumptions, then f (z) is also a periodic function, where n, k are positive integers.

引用

页码：1259 / 1267

页数：9

共 17 条

[1]

Baker I. N., 1966, ACTA SCI MATH SZEGED, V27, P197

[2]

Dong XJ, 2019, HOUSTON J MATH, V45, P1021

[3]

Gross F., 1971, RENT CRIC MAT PALERM, V21, P284, DOI DOI 10.1007/BF02843792

[4]

Hal?se G., 1972, PERIOD MATH HUNG, V2, P73, DOI DOI 10.1007/BF02018653

[5] Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity [J].

Heittokangas, J. ;

Korhonen, R. ;

Laine, I. ;

Rieppo, J. ;

Zhang, J. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 355 (01) :352-363

[6]

Li P, 2019, HOUSTON J MATH, V45, P431

[7] A NOTE ON THE PERIODICITY OF ENTIRE FUNCTIONS [J].

Liu, Kai ;

Yu, Peiyong .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2019, 100 (02) :290-296

[8] SOME RESULTS RELATED TO COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS OF CERTAIN TYPES [J].

Liu, Kai ;

Dong, Xianjing .

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2014, 51 (05) :1453-1467

[9] ON THE PERIODICITY OF TRANSCENDENTAL ENTIRE FUNCTIONS [J].

Liu, Xinling ;

Korhonen, Risto .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2020, 101 (03) :453-465

[10]

Ozawa M., 1977, KODAI MATH SEM REP, V29, P308

← 1 2 →