Chebyshevskii Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Chebyshevskii Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Chebyshevskii Sbornik, 2020, Volume 21, Issue 2, Pages 266–274
DOI: https://doi.org/10.22405/2226-8383-2018-21-2-266-274
(Mi cheb908)
 

About new examples of Serre curves

A. T. Lipkovskia, F. Yu. Popelenskyb

a Faculty of Mathematics, University of Belgrade (Belgrade, Serbia)
b Faculty of Mechanics and Mathematics of M. V. Lomonosov MSU (Moscow)
References:
Abstract: Abel's theorem claims that the Lemniscate can be divided into $n$ equal arcs by ruler and compass iff $n=2^kp_1\ldots p_m$, where $p_j$ are pairwise distinct Fermat primes. The proof is based on the fact that the lemniscate can be parametrised by rational functions and the arc length is a first type elliptic integral of the parameter. Joseph Alfred Serret proposed a method to describe all such curves in [1]. In papers [1, 2, 3] he found series of such curves and described its important properties. Since then no new examples of curves with rational parametrisation such that arc length is a first type elliptic integral of the parameter are known. In this note we describe new example of such a curve.
Keywords: Serret curve, elliptic integral, algebraic curve.
Received: 28.11.2019
Accepted: 11.03.2020
Document Type: Article
UDC: 512.772, 517.583
Language: Russian
Citation: A. T. Lipkovski, F. Yu. Popelensky, “About new examples of Serre curves”, Chebyshevskii Sb., 21:2 (2020), 266–274
Citation in format AMSBIB
\Bibitem{LipPop20}
\by A.~T.~Lipkovski, F.~Yu.~Popelensky
\paper About new examples of Serre curves
\jour Chebyshevskii Sb.
\yr 2020
\vol 21
\issue 2
\pages 266--274
\mathnet{http://mi.mathnet.ru/cheb908}
\crossref{https://doi.org/10.22405/2226-8383-2018-21-2-266-274}
Linking options:
  • https://www.mathnet.ru/eng/cheb908
  • https://www.mathnet.ru/eng/cheb/v21/i2/p266
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:101
    Full-text PDF :50
    References:19
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024