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http://hdl.handle.net/11701/17926
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Поле DC | Значение | Язык |
---|---|---|
dc.contributor.author | Antipov, Мikhail А. | - |
dc.contributor.author | Pimenov, Кonstantin I. | - |
dc.date.accessioned | 2020-05-28T13:44:39Z | - |
dc.date.available | 2020-05-28T13:44:39Z | - |
dc.date.issued | 2020-06 | - |
dc.identifier.citation | Antipov M.A., Pimenov K. I. Ramanujan denesting formulae for cubic radicals. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 2, pp. 187–196. | en_GB |
dc.identifier.other | https://doi.org/10.21638/11701/spbu01.2020.201 | - |
dc.identifier.uri | http://hdl.handle.net/11701/17926 | - |
dc.description.abstract | This paper contains an explanation of Ramanujan-type formulas with cubic radicals of cubic irrationalities in the situation when these radicals are contained in a pure cubic extension. We give a complete description of formulas of such type, answering the Zippel’s question. It turns out that Ramanujan-type formulas are in some sense unique in this situation. In particular, there must be no more than three summands in the right-hand side and the norm of the irrationality in question must be a cube. In this situation we associate with cubic irrationalities a cyclic cubic polinomial, which is reducible if and only if one can simplify the corresponding cubic radical. This correspondence is inverse to the so-called Ramanujan correspondence defined in the preceding papers, where one associates a pure cubic extension to some cyclic polinomial. | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | St Petersburg State University | en_GB |
dc.relation.ispartofseries | Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 2 | - |
dc.subject | Ramanujan formulas | en_GB |
dc.subject | simplification of radicals | en_GB |
dc.subject | Ramanujan correspondence | en_GB |
dc.title | Ramanujan denesting formulae for cubic radicals | en_GB |
dc.type | Article | en_GB |
Располагается в коллекциях: | Issue 2 |
Файлы этого ресурса:
Файл | Описание | Размер | Формат | |
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187-196.pdf | 320,38 kB | Adobe PDF | Просмотреть/Открыть |
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