Modular Form Representation for Periods of Hyperelliptic Integrals
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 on...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147719 |
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| Cite this: | Modular Form Representation for Periods of Hyperelliptic Integrals / K. Eilers // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 10 назв. — англ. |
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Eilers, K. 2019-02-15T18:37:46Z 2019-02-15T18:37:46Z 2016 Modular Form Representation for Periods of Hyperelliptic Integrals / K. Eilers // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 10 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14H42; 30F30 DOI:10.3842/SIGMA.2016.060 https://nasplib.isofts.kiev.ua/handle/123456789/147719 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Modular Form Representation for Periods of Hyperelliptic Integrals Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Modular Form Representation for Periods of Hyperelliptic Integrals |
| spellingShingle |
Modular Form Representation for Periods of Hyperelliptic Integrals Eilers, K. |
| title_short |
Modular Form Representation for Periods of Hyperelliptic Integrals |
| title_full |
Modular Form Representation for Periods of Hyperelliptic Integrals |
| title_fullStr |
Modular Form Representation for Periods of Hyperelliptic Integrals |
| title_full_unstemmed |
Modular Form Representation for Periods of Hyperelliptic Integrals |
| title_sort |
modular form representation for periods of hyperelliptic integrals |
| author |
Eilers, K. |
| author_facet |
Eilers, K. |
| publishDate |
2016 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147719 |
| citation_txt |
Modular Form Representation for Periods of Hyperelliptic Integrals / K. Eilers // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 10 назв. — англ. |
| work_keys_str_mv |
AT eilersk modularformrepresentationforperiodsofhyperellipticintegrals |
| first_indexed |
2025-12-07T13:19:37Z |
| last_indexed |
2025-12-07T13:19:37Z |
| _version_ |
1850855734726623232 |