Askey-Wilson version of Second Main Theorem for holomorphic curves in projective space

TL;DR

This paper develops an Askey-Wilson operator-based version of the Second Main Theorem for holomorphic curves in projective space, improving previous results and incorporating hypersurface components.

Contribution

It introduces an Askey-Wilson Wronskian-Casorati determinant and extends the Second Main Theorem to include hypersurfaces in subgeneral position.

Findings

Established an Askey-Wilson version of the Second Main Theorem.

Extended the theorem to account for hypersurfaces in subgeneral position.

Improved upon previous results by Chiang and Feng.

Abstract

In this paper, an Askey-Wilson version of the Wronskian-Casorati determinant $\mathcal{W}(f_{0}, \dots, f_{n})(x)$ for meromorphic functions $f_{0}, \dots, f_{n}$ 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.