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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2016 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147719 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Modular Form Representation for Periods of Hyperelliptic Integrals / K. Eilers // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 10 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862619868333867008 |
|---|---|
| author | Eilers, K. |
| author_facet | Eilers, K. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T13:19:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147719 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:19:37Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Modular Form Representation for Periods of Hyperelliptic Integrals Eilers, K. |
| title | 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_short | Modular Form Representation for Periods of Hyperelliptic Integrals |
| title_sort | modular form representation for periods of hyperelliptic integrals |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147719 |
| work_keys_str_mv | AT eilersk modularformrepresentationforperiodsofhyperellipticintegrals |