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Modular Form Representation for Periods of Hyperelliptic Integrals
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Modular Form Representation for Periods of Hyperelliptic Integrals
Інший ID:
2010 Mathematics Subject Classification: 14H42; 30F30
DOI:10.3842/SIGMA.2016.060
DOI:10.3842/SIGMA.2016.060
Посилання:
Modular Form Representation for Periods of Hyperelliptic Integrals / K. Eilers // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 10 назв. — англ.
Підтримка:
The author is grateful to V. Enolski for useful discussion and constant interest to the work,
and also to all referees, whose comments promoted a further improvement of the text. In especially
the author wants to mention the contribution of the anonymous referee, who reported
formula (5.3) and reminded us of Fay’s Corollary 2.12 [7], which essentially improved our initial
statements. Also the author gratefully acknowledges the Deutsche Forschungsgemeinschaft
(DFG) for financial support within the framework of the DFG Research Training group 1620
Models of gravity.
Дата:
2016
Переглядів:
520
Завантажень:
308
Анотація:
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 λj 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.
