Non-real zeros of derivatives of real meromorphic functions of infinite order

2010 ◽  
Vol 150 (2) ◽  
pp. 343-351 ◽  
Author(s):  
J. K. LANGLEY
Keyword(s):  
Meromorphic Function ◽  
Infinite Order ◽  
Meromorphic Functions ◽  
Real Zeros ◽  
Derivatives Of ◽  
Real Poles ◽  
Zeros Of Derivatives

AbstractLet f be a real meromorphic function of infinite order in the plane, with finitely many zeros and non-real poles. Then f″ has infinitely many non-real zeros.

Non-real zeros of real differential polynomials

2011 ◽  
Vol 141 (3) ◽  
pp. 631-639 ◽  
Author(s):  
J. K. Langley
Keyword(s):  
Lower Order ◽  
Meromorphic Functions ◽  
Differential Polynomials ◽  
Real Zeros ◽  
Derivatives Of ◽  
Real Poles ◽  
Finite Lower Order

The main results of the paper determine all real meromorphic functions f of finite lower order in the plane such that f has finitely many zeros and non-real poles and such that certain combinations of derivatives of f have few non-real zeros.

scholarly journals Derivatives of Meromorphic Functions with Multiple Zeros and Small Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Pai Yang ◽  
Peiyan Niu
Keyword(s):  
Meromorphic Function ◽  
Rational Function ◽  
Elliptic Function ◽  
Meromorphic Functions ◽  
Infinitely Many Solutions ◽  
Multiple Zeros ◽  
Small Functions ◽  
Derivatives Of

Letfzbe a meromorphic function inℂ, and letαz=Rzhz≢0, wherehzis a nonconstant elliptic function andRzis a rational function. Suppose that all zeros offzare multiple except finitely many andTr,α=oTr,fasr→∞. Thenf'z=αzhas infinitely many solutions.

Sign in / Sign up

Export Citation Format

Share Document