The Ramificant Determinant
We give an introduction to the transalgebraic theory of simply connected log-Riemann surfaces with a finite number of infinite ramification points (transalgebraic curves of genus 0). We define the base vector space of transcendental functions and establish, by elementary methods, some transcendental...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210302 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Ramificant Determinant / K. Biswas, R. Pérez-Marco // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 19 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-210302 |
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Biswas, K. Pérez-Marco, R. 2025-12-05T09:27:25Z 2019 The Ramificant Determinant / K. Biswas, R. Pérez-Marco // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 30F99; 30D99 arXiv: 1903.06770 https://nasplib.isofts.kiev.ua/handle/123456789/210302 https://doi.org/10.3842/SIGMA.2019.086 We give an introduction to the transalgebraic theory of simply connected log-Riemann surfaces with a finite number of infinite ramification points (transalgebraic curves of genus 0). We define the base vector space of transcendental functions and establish, by elementary methods, some transcendental properties. We introduce the Ramificant determinant constructed with transcendental periods, and we give a closed-form formula that gives the main applications to transalgebraic curves. We prove an Abel-like theorem and a Torelli-like theorem. Transposing to the transalgebraic curve, the base vector space of transcendental functions, they generate the structural ring from which the points of the transalgebraic curve can be recovered algebraically, including infinite ramification points. We are grateful to Y. Levagnini and the referees for their careful reading and corrections that improved the article. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Ramificant Determinant Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The Ramificant Determinant |
| spellingShingle |
The Ramificant Determinant Biswas, K. Pérez-Marco, R. |
| title_short |
The Ramificant Determinant |
| title_full |
The Ramificant Determinant |
| title_fullStr |
The Ramificant Determinant |
| title_full_unstemmed |
The Ramificant Determinant |
| title_sort |
ramificant determinant |
| author |
Biswas, K. Pérez-Marco, R. |
| author_facet |
Biswas, K. Pérez-Marco, R. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We give an introduction to the transalgebraic theory of simply connected log-Riemann surfaces with a finite number of infinite ramification points (transalgebraic curves of genus 0). We define the base vector space of transcendental functions and establish, by elementary methods, some transcendental properties. We introduce the Ramificant determinant constructed with transcendental periods, and we give a closed-form formula that gives the main applications to transalgebraic curves. We prove an Abel-like theorem and a Torelli-like theorem. Transposing to the transalgebraic curve, the base vector space of transcendental functions, they generate the structural ring from which the points of the transalgebraic curve can be recovered algebraically, including infinite ramification points.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210302 |
| citation_txt |
The Ramificant Determinant / K. Biswas, R. Pérez-Marco // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 19 назв. — англ. |
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2025-12-07T21:25:04Z |
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2025-12-07T21:25:04Z |
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