title: Ramanujan denesting formulae for cubic radicals
metadata.name: dc.contributor.author
metadata.value: Antipov, Мikhail А.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Pimenov, Кonstantin I.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-05-28T13:44:39Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-05-28T13:44:39Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.201
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17926
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: Ramanujan formulas
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: simplification of radicals
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Ramanujan correspondence
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Ramanujan denesting formulae for cubic radicals
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 187-196.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17926/1/187-196.pdf
resources.format: Adobe PDF
resources.size: 320,38 kB