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摘要
This paper is dedicated to provide theta function representation of algebro-geometric solutions and related crucial quantities for the complex Sharma-Tasso-Olver (CSTO) hierarchy. Our main tools include the polynomial recursive formalism to derive the CSTO hierarchy, the hyper-elliptic curve with finite number of genus, the Baker-Akhiezer functions, the meromorphic function, the Dubrovin-type equations for auxiliary divisors, and the associated trace formulas. By use of these tools, the explicit representations of the Baker-Ahhiezer functions, the meromorphic function, and the algebro-geometric solutions are obtained for the entire CSTO hierarchy.
