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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 470, Pages 5–20 (Mi znsl6608)  
This article is cited in 1 scientific paper (total in 1 paper)

On certain multiplicative structures on cubic extensions

M. A. Antipov, K. I. Pimenov

St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (217 kB) Citations (1)
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Abstract: Multiplicative properties of a certain correspondence between elements in cyclic cubic extension of rational number field and elements in adjusted pure cubic extensions are investigated. Shanks cubic polynomial case is considered to connect multiplication of pure cubic irrationals with a point summation on an associated elliptic curve.
Key words and phrases: cyclic cubic extension, surds, Ramanujan notebooks, Fermat elliptic curve.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00750
Received: 25.06.2018
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 243, Issue 4, Pages 505–514
DOI: https://doi.org/10.1007/s10958-019-04552-y
Bibliographic databases:
Document Type: Article
UDC: 512.623.22+511.14
Language: Russian
Citation: M. A. Antipov, K. I. Pimenov, “On certain multiplicative structures on cubic extensions”, Problems in the theory of representations of algebras and groups. Part 33, Zap. Nauchn. Sem. POMI, 470, POMI, St. Petersburg, 2018, 5–20; J. Math. Sci. (N. Y.), 243:4 (2019), 505–514
Citation in format AMSBIB
\Bibitem{AntPim18}
\by M.~A.~Antipov, K.~I.~Pimenov
\paper On certain multiplicative structures on cubic extensions
\inbook Problems in the theory of representations of algebras and groups. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 470
\pages 5--20
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6608}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 243
\issue 4
\pages 505--514
\crossref{https://doi.org/10.1007/s10958-019-04552-y}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074474379}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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