Building Abelian Functions with Generalised Baker-Hirota Operators
We present a new systematic method to construct Abelian functions on Jacobian varieties of plane, algebraic curves. The main tool used is a symmetric generalisation of the bilinear operator defined in the work of Baker and Hirota. We give explicit formulae for the multiple applications of the operat...
Збережено в:
| Дата: | 2012 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148444 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Building Abelian Functions with Generalised Baker-Hirota Operators / M. England, Ch. Athorne // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 36 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148444 |
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dspace |
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irk-123456789-1484442019-02-19T01:23:12Z Building Abelian Functions with Generalised Baker-Hirota Operators England, M. Athorne, C. We present a new systematic method to construct Abelian functions on Jacobian varieties of plane, algebraic curves. The main tool used is a symmetric generalisation of the bilinear operator defined in the work of Baker and Hirota. We give explicit formulae for the multiple applications of the operators, use them to define infinite sequences of Abelian functions of a prescribed pole structure and deduce the key properties of these functions. We apply the theory on the two canonical curves of genus three, presenting new explicit examples of vector space bases of Abelian functions. These reveal previously unseen similarities between the theories of functions associated to curves of the same genus. 2012 Article Building Abelian Functions with Generalised Baker-Hirota Operators / M. England, Ch. Athorne // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 36 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14H40; 14H50; 14H70 DOI: http://dx.doi.org/10.3842/SIGMA.2012.037 http://dspace.nbuv.gov.ua/handle/123456789/148444 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We present a new systematic method to construct Abelian functions on Jacobian varieties of plane, algebraic curves. The main tool used is a symmetric generalisation of the bilinear operator defined in the work of Baker and Hirota. We give explicit formulae for the multiple applications of the operators, use them to define infinite sequences of Abelian functions of a prescribed pole structure and deduce the key properties of these functions. We apply the theory on the two canonical curves of genus three, presenting new explicit examples of vector space bases of Abelian functions. These reveal previously unseen similarities between the theories of functions associated to curves of the same genus. |
| format |
Article |
| author |
England, M. Athorne, C. |
| spellingShingle |
England, M. Athorne, C. Building Abelian Functions with Generalised Baker-Hirota Operators Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
England, M. Athorne, C. |
| author_sort |
England, M. |
| title |
Building Abelian Functions with Generalised Baker-Hirota Operators |
| title_short |
Building Abelian Functions with Generalised Baker-Hirota Operators |
| title_full |
Building Abelian Functions with Generalised Baker-Hirota Operators |
| title_fullStr |
Building Abelian Functions with Generalised Baker-Hirota Operators |
| title_full_unstemmed |
Building Abelian Functions with Generalised Baker-Hirota Operators |
| title_sort |
building abelian functions with generalised baker-hirota operators |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148444 |
| citation_txt |
Building Abelian Functions with Generalised Baker-Hirota Operators / M. England, Ch. Athorne // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 36 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT englandm buildingabelianfunctionswithgeneralisedbakerhirotaoperators AT athornec buildingabelianfunctionswithgeneralisedbakerhirotaoperators |
| first_indexed |
2023-05-20T17:30:41Z |
| last_indexed |
2023-05-20T17:30:41Z |
| _version_ |
1796153458145886208 |