О кубических формулах Рамануджана упрощения вложенных радикалов

M. A. Antipov, K. I. Pimenov

Research output: Contribution to journalArticlepeer-review

Abstract

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 cubic irrationalities with a cyclic cubic polynomial, 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 polynomial.

Original languageRussian
Pages (from-to)115-121
Number of pages7
JournalVestnik St. Petersburg University: Mathematics
Volume53
Issue number2
DOIs
StatePublished - 1 Apr 2020

Scopus subject areas

  • Mathematics(all)

Keywords

  • Ramanujan correspondence
  • Ramanujan formulas
  • simplification of radicals

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