Cartan’s Second Main Theorem and Mason’s Theorem for Jackson Difference Operator

Abstract

Let f: ℂ → ℙ ⁿ be a holomorphic curve of order zero. The authors establish a Jackson difference analogue of Cartan’s second main theorem for the Jackson q-Casorati determinant and introduce a truncated second main theorem of Jackson difference operator for holomorphic curves. In addition, a Jackson difference Mason’s theorem is proved by using a Jackson difference radical of a polynomial. Furthermore, they extend the Mason’s theorem for m + 1 polynomials. Some examples are constructed to show that their results are accurate.

Keywords

Jackson difference operator / Nevanlinna theory / Holomorphic curve / Cartan’s second main theorem / Mason’s theorem / Polynomial

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