A lower bound for the number of zeros of a meromorphic function and its second derivative

被引：11

作者：

Langley, JK ^{[1
]}

机构：

[1] UNIV NOTTINGHAM,NOTTINGHAM NG7 2RD,ENGLAND

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 1996年 / 39卷

关键词：

D O I：

10.1017/S0013091500022884

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for a function f(z) transcendental and meromorphic in the plane and not of the form exp(az+b), we have either N(r,1/ff'')not equal 0(T(r,f'/f)) or (r-->infinity)lim log N(r,1/ff '')/loglogr greater than or equal to 2.

引用

页码：171 / 185

页数：15

共 50 条

[41] On The Growth Of An E-Valued Meromorphic Function And Its Derivative
Pujari, Veena L.
APPLIED MATHEMATICS E-NOTES, 2015, 15 : 137 - 146
[42] Meromorphic Function Sharing Two Small Functions with Its Derivative
Liu, Kai
Qi, Xiao-guang
KYUNGPOOK MATHEMATICAL JOURNAL, 2009, 49 (02): : 235 - 243
[43] AN IMPROVED LOWER BOUND FOR THE EXPECTED NUMBER OF REAL ZEROS OF A RANDOM ALGEBRAIC POLYNOMIALS
CHRISTENSEN, MJ
SAMBANDHAM, M
STOCHASTIC ANALYSIS AND APPLICATIONS, 1984, 2 (04) : 431 - 436
[44] LOGARITHMIC DERIVATIVE OF A MEROMORPHIC FUNCTION
GOLDBERG, AA
GRINSHTEIN, VA
MATHEMATICAL NOTES, 1976, 19 (3-4) : 320 - 323
[45] A lower bound in an approximation problem involving the zeros of the Riemann zeta function
Burnol, JF
ADVANCES IN MATHEMATICS, 2002, 170 (01) : 56 - 70
[46] LOWER BOUND FOR ZEROS OF RIEMANN'S ZETA FUNCTION ON σ=1/2
楼世拓
姚琦
A Monthly Journal of Science, 1980, (05) : 374 - 377
[47] A power of a meromorphic function sharing a small function IM with its first derivative
Indrajit Lahiri
Sujoy Majumder
Bollettino dell'Unione Matematica Italiana, 2020, 13 : 113 - 130
[48] On the uniqueness of a power of a meromorphic function sharing a small function with the power of its derivative
Banerjee, Abhijit
Majumder, Sujoy
COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2010, 51 (04): : 565 - 576
[49] A power of a meromorphic function sharing a small function IM with its first derivative
Lahiri, Indrajit
Majumder, Sujoy
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2020, 13 (01): : 113 - 130
[50] The zeros of the first two derivatives of a meromorphic function
Langley, JK
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 124 (08) : 2439 - 2441

← 1 2 3 4 5 →