%0 Journal Article
%T 具有权弱分担值的微分多项式的亚纯函数的唯一性<br>The Uniqueness of Meromorphic Functions of the Differential Polynomials with the Weakly Weighted Sharing Value
%A 吴琳琳
%J Pure Mathematics
%P 55-69
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.152046
%X 本文研究了一个形如<math xmlns='http://www.w3.org/1998/Math/MathML'>
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   <mi>n</mi>
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     <mi>f</mi>
     <mi>m</mi>
    </msup>
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     <mi>z</mi>
    <mo>)</mo></mrow><mo>+</mo><mi>&#x03B2;</mi></mrow>
  <mo>)</mo></mrow></mrow>
</math>

的亚纯函数的<i>k</i>阶导数及其移动算子的<i>k</i>阶导数权弱分担值的唯一性问题&#65292;其中<math xmlns='http://www.w3.org/1998/Math/MathML'>
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  <mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>k</mi></mrow>
</math>

均是正整数&#65292;<math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>&#x03B1;</mi><mo>,</mo><mi>&#x03B2;</mi></mrow>
</math>

是满足<math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mrow><mo>|</mo> <mi>&#x03B1;</mi> <mo>|</mo></mrow><mo>+</mo><mrow><mo>|</mo> <mi>&#x03B2;</mi> <mo>|</mo></mrow><mo>&#x2260;</mo><mn>0</mn></mrow>
</math>

的常数&#65292;将2018年林珊华和林伟川提出的结果推广到更一般的形式。<br>In this paper, we study the uniqueness problem of the weakly weighted sharing values for the <i>k</i>-th derivative of a meromorphic function of the form <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <msup>
   <mi>f</mi>
   <mi>n</mi>
  </msup>
  <mrow><mo>(</mo>
   <mi>z</mi>
  <mo>)</mo></mrow><mrow><mo>(</mo>
   <mrow>
    <mi>&#x03B1;</mi><msup>
     <mi>f</mi>
     <mi>m</mi>
    </msup>
    <mrow><mo>(</mo>
     <mi>z</mi>
    <mo>)</mo></mrow><mo>+</mo><mi>&#x03B2;</mi></mrow>
  <mo>)</mo></mrow></mrow>
</math>

 and the <i>k</i>-th derivative of its translation operator, where <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>k</mi></mrow>
</math>

 are all positive integers, and <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>&#x03B1;</mi><mo>,</mo><mi>&#x03B2;</mi></mrow>
</math>

 are constants satisfying <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mrow><mo>|</mo> <mi>&#x03B1;</mi> <mo>|</mo></mrow><mo>+</mo><mrow><mo>|</mo> <mi>&#x03B2;</mi> <mo>|</mo></mrow><mo>&#x2260;</mo><mn>0</mn></mrow>
</math>

 the results proposed by Lin Shanhua and Lin Weichuan in 2018 are extended to a more general form.
%K 微分多项式&#65292
%K 亚纯函数&#65292
%K 权弱分担&#65292
%K 唯一性定理<br>Differential Polynomials
%K Meromorphic Functions
%K Weakly Weighted Sharing
%K Uniqueness Theorems
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=107571