Modular Form Representation for Periods of Hyperelliptic Integrals

[摘要] To every hyperelliptic curve one can assign the periods of the integrals over the holomorphic and the meromorphic differentials. By comparing two representations of the so-called projective connection it is possible to reexpress the latter periods by the first. This leads to expressions including only the curve's parameters $\lambda_j$ and modular forms. By a change of basis of the meromorphic differentials one can further simplify this expression. We discuss the advantages of these explicitly given bases, which we call Baker and Klein basis , respectively.

[关键词] periods of second kind dif ferentials;theta-constants;modular forms