Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials
Two problems are addressed: reduction of an arbitrary degree non-special divisor to the equivalent divisor of the degree equal to the genus of a curve, and addition of divisors of arbitrary degrees. The hyperelliptic case is considered the simplest model. Explicit formulas defining reduced divisors...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210697 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials. Julia Bernatska and Yaacov Kopeliovich. SIGMA 16 (2020), 053, 21 pages |
Репозитарії
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nasplib_isofts_kiev_ua-123456789-210697 |
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Bernatska, Julia Kopeliovich, Yaacov 2025-12-15T15:23:06Z 2020 Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials. Julia Bernatska and Yaacov Kopeliovich. SIGMA 16 (2020), 053, 21 pages 1815-0659 2020 Mathematics Subject Classification: 32Q30; 14G50 arXiv:1912.13277 https://nasplib.isofts.kiev.ua/handle/123456789/210697 https://doi.org/10.3842/SIGMA.2020.053 Two problems are addressed: reduction of an arbitrary degree non-special divisor to the equivalent divisor of the degree equal to the genus of a curve, and addition of divisors of arbitrary degrees. The hyperelliptic case is considered the simplest model. Explicit formulas defining reduced divisors for some particular cases are found. The reduced divisors are obtained in the form of a solution of the Jacobi inversion problem, which provides a way of computing Abelian functions on arbitrary non-special divisors. An effective reduction algorithm is proposed, which has the advantage that it involves only arithmetic operations on polynomials. The proposed addition algorithm contains more details compared with the known in cryptography, and is extended to divisors of arbitrary degrees compared with the known in the theory of hyperelliptic functions. The authors are thankful to the referees for the comments that have improved the paper substantially. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials |
| spellingShingle |
Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials Bernatska, Julia Kopeliovich, Yaacov |
| title_short |
Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials |
| title_full |
Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials |
| title_fullStr |
Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials |
| title_full_unstemmed |
Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials |
| title_sort |
addition of divisors on hyperelliptic curves via interpolation polynomials |
| author |
Bernatska, Julia Kopeliovich, Yaacov |
| author_facet |
Bernatska, Julia Kopeliovich, Yaacov |
| publishDate |
2020 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Two problems are addressed: reduction of an arbitrary degree non-special divisor to the equivalent divisor of the degree equal to the genus of a curve, and addition of divisors of arbitrary degrees. The hyperelliptic case is considered the simplest model. Explicit formulas defining reduced divisors for some particular cases are found. The reduced divisors are obtained in the form of a solution of the Jacobi inversion problem, which provides a way of computing Abelian functions on arbitrary non-special divisors. An effective reduction algorithm is proposed, which has the advantage that it involves only arithmetic operations on polynomials. The proposed addition algorithm contains more details compared with the known in cryptography, and is extended to divisors of arbitrary degrees compared with the known in the theory of hyperelliptic functions.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210697 |
| citation_txt |
Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials. Julia Bernatska and Yaacov Kopeliovich. SIGMA 16 (2020), 053, 21 pages |
| work_keys_str_mv |
AT bernatskajulia additionofdivisorsonhyperellipticcurvesviainterpolationpolynomials AT kopeliovichyaacov additionofdivisorsonhyperellipticcurvesviainterpolationpolynomials |
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2025-12-17T12:04:31Z |
| last_indexed |
2025-12-17T12:04:31Z |
| _version_ |
1851756979341492225 |