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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Periods of second kind differentials of $(n,s)$-curves
J. C. Eilbeckab, K. Eilersc, V. Z. Enolskiadb a Department of Mathematics, Heriot-Watt University, Edinburgh, UK
b Maxwell Institute for Mathematical Sciences
c Faculty of Mathematics, University of Oldenburg, Germany
d Institute of Magnetism, National Academy of Sciences of Ukraine, Kiev, 03142, Ukraine
Аннотация:
For elliptic curves expressions for the periods of elliptic integrals of the second kind in terms of theta-constants, have been known since the middle of the 19th century. In this paper we consider the problem of generalizing these results to curves of higher genera, in particular to a special class of algebraic curves, the so-called $(n,s)$-curves. It is shown that the representations required can be obtained by the comparison of two equivalent expressions for the projective connection, one due to Fay–Wirtinger and the other from Klein–Weierstrass. As a principle example, we consider the case of the genus two hyperelliptic curve, and a number of new Thomae and Rosenhain type formulae are obtained. We anticipate that our analysis for the genus two curve can be extended to higher genera hyperelliptic curves, as well as to other classes of $(n,s)$ non-hyperelliptic curves. References: 33 entries.
Ключевые слова и фразы:
moduli of algebraic curves, theta-constants, sigma-functions.
Полный текст:
PDF файл (362 kB)
Список литературы:
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Англоязычная версия:
Transactions of the Moscow Mathematical Society, 2013, 74, 245–260
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Тип публикации:
Статья
УДК:
515.178.2+517.958+514
MSC: 32G15, 14K25, 30F30 Поступила в редакцию: 14.05.2013
Язык публикации: английский
Образец цитирования:
J. C. Eilbeck, K. Eilers, V. Z. Enolski, “Periods of second kind differentials of $(n,s)$-curves”, Тр. ММО, 74, no. 2, МЦНМО, М., 2013, 297–315; Trans. Moscow Math. Soc., 74 (2013), 245–260
Цитирование в формате AMSBIB
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Образцы ссылок на эту страницу:
http://mi.mathnet.ru/mmo550 http://mi.mathnet.ru/rus/mmo/v74/i2/p297
Citing articles on Google Scholar:
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Эта публикация цитируется в следующих статьяx:
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Keno Eilers, “Modular Form Representation for Periods of Hyperelliptic Integrals”, SIGMA, 12 (2016), 060, 13 pp.
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