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
Date:2016
Main Author: Eilers, K.
Format: Article
Language:English
Published: Інститут математики НАН України 2016
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147719
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-147719
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.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Modular Form Representation for Periods of Hyperelliptic Integrals
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
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
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