Geodesic
Modular Form Representation for Periods of Hyperelliptic Integrals
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: periods of second kind differentials; theta-constants; modular forms. 
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     author = {Keno Eilers},
     title = {Modular {Form} {Representation} for {Periods} of {Hyperelliptic} {Integrals}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a59/}
}
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Keno Eilers. Modular Form Representation for Periods of Hyperelliptic Integrals. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a59/

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