FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4324264985> ?p ?o ?g. }

• W4324264985 abstract "Abstract In this article, we study some results on the value distribution of differential polynomials and mainly prove the following theorem: suppose that <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>P</m:mi> </m:math> P is a polynomial with <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi mathvariant=normal>deg</m:mi> <m:mspace width=0.33em /> <m:mi>P</m:mi> <m:mo>≥</m:mo> <m:mn>3</m:mn> </m:math> {rm{deg }}hspace{0.33em}Pge 3 and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>f</m:mi> </m:math> f is a transcendental meromorphic function. Let <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>α</m:mi> </m:math> alpha be a small function of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>f</m:mi> </m:math> f . If <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>α</m:mi> </m:math> alpha is a constant, we also require that there exists a constant <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>A</m:mi> <m:mo>≠</m:mo> <m:mi>α</m:mi> </m:math> Ane alpha such that <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>P</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>−</m:mo> <m:mi>A</m:mi> </m:math> Pleft(z)-A has a zero of multiplicity at least 3. Then, for any <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mn>0</m:mn> <m:mo><</m:mo> <m:mi>ε</m:mi> <m:mo><</m:mo> <m:mn>1</m:mn> </m:math> 0lt varepsilon lt 1 , we have <m:math xmlns:m=http://www.w3.org/1998/Math/MathML display=block> <m:mi>T</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>r</m:mi> <m:mo>,</m:mo> <m:mi>f</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>≤</m:mo> <m:mi>k</m:mi> <m:mover accent=true> <m:mrow> <m:mi>N</m:mi> </m:mrow> <m:mrow> <m:mo stretchy=true>¯</m:mo> </m:mrow> </m:mover> <m:mfenced open=( close=)> <m:mrow> <m:mi>r</m:mi> <m:mo>,</m:mo> <m:mfrac> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mrow> <m:mi>P</m:mi> <m:mrow> <m:mrow> <m:mo>(</m:mo> </m:mrow> <m:mrow> <m:mi>f</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>−</m:mo> <m:mi>α</m:mi> </m:mrow> </m:mfrac> </m:mrow> </m:mfenced> <m:mo>+</m:mo> <m:mi>S</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>r</m:mi> <m:mo>,</m:mo> <m:mi>f</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> </m:math> Tleft(r,f)le koverline{N}left(r,frac{1}{P(f)-alpha }right)+Sleft(r,f), where if <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>P</m:mi> <m:mo accent=false>′</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> P^{prime} left(z) has only one zero, then <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>k</m:mi> <m:mo>=</m:mo> <m:mfrac> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mrow> <m:mi mathvariant=normal>deg</m:mi> <m:mspace width=0.33em /> <m:mi>P</m:mi> <m:mo>−</m:mo> <m:mn>2</m:mn> </m:mrow> </m:mfrac> </m:math> k=frac{1}{{rm{deg }}hspace{0.33em}P-2} ; if <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>P</m:mi> <m:mo accent=false>′</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> P^{prime} left(z) has two distinct zeros <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>a</m:mi> </m:math> a and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>b</m:mi> </m:math> b with <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>P</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>≠</m:mo> <m:mi>P</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>b</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> Pleft(a)ne Pleft(b) and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>α</m:mi> </m:math> alpha is nonconstant, then <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>k</m:mi> <m:mo>=</m:mo> <m:mfrac> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mrow> <m:mn>1</m:mn> <m:mo>−</m:mo> <m:mi>ε</m:mi> </m:mrow> </m:mfrac> </m:math> k=frac{1}{1-varepsilon } ; otherwise <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>k</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> </m:math> k=1 ." @default.
• W4324264985 created "2023-03-16" @default.
• W4324264985 creator A5017669233 @default.
• W4324264985 creator A5021578194 @default.
• W4324264985 creator A5053148906 @default.
• W4324264985 date "2023-01-01" @default.
• W4324264985 modified "2023-09-23" @default.
• W4324264985 title "Some results on the value distribution of differential polynomials" @default.
• W4324264985 cites W1530798444 @default.
• W4324264985 cites W2008832533 @default.
• W4324264985 cites W2013295017 @default.
• W4324264985 cites W2052516944 @default.
• W4324264985 cites W2056619679 @default.
• W4324264985 cites W2062339481 @default.
• W4324264985 cites W2062969908 @default.
• W4324264985 cites W2085346221 @default.
• W4324264985 cites W2115360563 @default.
• W4324264985 cites W2321146739 @default.
• W4324264985 cites W4244526423 @default.
• W4324264985 doi "https://doi.org/10.1515/math-2022-0560" @default.
• W4324264985 hasPublicationYear "2023" @default.
• W4324264985 type Work @default.
• W4324264985 citedByCount "0" @default.
• W4324264985 crossrefType "journal-article" @default.
• W4324264985 hasAuthorship W4324264985A5017669233 @default.
• W4324264985 hasAuthorship W4324264985A5021578194 @default.
• W4324264985 hasAuthorship W4324264985A5053148906 @default.
• W4324264985 hasBestOaLocation W43242649851 @default.
• W4324264985 hasConcept C114614502 @default.
• W4324264985 hasConcept C33923547 @default.
• W4324264985 hasConceptScore W4324264985C114614502 @default.
• W4324264985 hasConceptScore W4324264985C33923547 @default.
• W4324264985 hasIssue "1" @default.
• W4324264985 hasLocation W43242649851 @default.
• W4324264985 hasOpenAccess W4324264985 @default.
• W4324264985 hasPrimaryLocation W43242649851 @default.
• W4324264985 hasRelatedWork W1587224694 @default.
• W4324264985 hasRelatedWork W1978042415 @default.
• W4324264985 hasRelatedWork W1979597421 @default.
• W4324264985 hasRelatedWork W2007980826 @default.
• W4324264985 hasRelatedWork W2061531152 @default.
• W4324264985 hasRelatedWork W2077600819 @default.
• W4324264985 hasRelatedWork W2911598644 @default.
• W4324264985 hasRelatedWork W3002753104 @default.
• W4324264985 hasRelatedWork W4225152035 @default.
• W4324264985 hasRelatedWork W4245490552 @default.
• W4324264985 hasVolume "21" @default.
• W4324264985 isParatext "false" @default.
• W4324264985 isRetracted "false" @default.
• W4324264985 workType "article" @default.