<p>In this paper, an Askey-Wilson version of the Wronskian-Casorati determinant <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {W}(f_{0}, \dots , f_{n})(x)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">W</mi> <mrow> <mo stretchy="false">(</mo> <msub> <mi>f</mi> <mn>0</mn> </msub> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <msub> <mi>f</mi> <mi>n</mi> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for meromorphic functions <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(f_{0}, \dots , f_{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>f</mi> <mn>0</mn> </msub> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <msub> <mi>f</mi> <mi>n</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> is introduced to establish an Askey-Wilson version of the general form of the Second Main Theorem in projective space. This improves upon the original Second Main Theorem for the Askey-Wilson operator due to Chiang and Feng. In addition, by taking into account the number of irreducible components of hypersurfaces, an Askey-Wilson version of the Truncated Second Main Theorem for holomorphic curves into projective space with hypersurfaces located in <i>l</i>-subgeneral position is obtained.</p>

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Askey-Wilson Version of Second Main Theorem for Holomorphic Curves in Projective Space

  • Chengliang Tan,
  • Risto Korhonen

摘要

In this paper, an Askey-Wilson version of the Wronskian-Casorati determinant \(\mathcal {W}(f_{0}, \dots , f_{n})(x)\) W ( f 0 , , f n ) ( x ) for meromorphic functions \(f_{0}, \dots , f_{n}\) f 0 , , f n is introduced to establish an Askey-Wilson version of the general form of the Second Main Theorem in projective space. This improves upon the original Second Main Theorem for the Askey-Wilson operator due to Chiang and Feng. In addition, by taking into account the number of irreducible components of hypersurfaces, an Askey-Wilson version of the Truncated Second Main Theorem for holomorphic curves into projective space with hypersurfaces located in l-subgeneral position is obtained.