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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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Інститут математики НАН України
2016
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/147719 |
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irk-123456789-1477192019-02-16T01:24:22Z Modular Form Representation for Periods of Hyperelliptic Integrals Eilers, K. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147719 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| 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. |
| format |
Article |
| author |
Eilers, K. |
| spellingShingle |
Eilers, K. Modular Form Representation for Periods of Hyperelliptic Integrals Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Eilers, K. |
| author_sort |
Eilers, K. |
| title |
Modular Form Representation for Periods of Hyperelliptic Integrals |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT eilersk modularformrepresentationforperiodsofhyperellipticintegrals |
| first_indexed |
2023-05-20T17:28:08Z |
| last_indexed |
2023-05-20T17:28:08Z |
| _version_ |
1796153370556235776 |