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



Dokl. Akad. Nauk:
Year:
Volume:
Issue:
Page:
Find






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


Dokl. Akad. Nauk, 2018, Volume 483, Number 6, Pages 609–613 (Mi dan46857)  

On the Finiteness of Hyperelliptic Fields with Special Properties and Periodic Expansion of $\sqrt f$

V. P. Platonov, M. M. Petrunin, V. S. Zhgoon, Yu. N. Shteinikov

Scientific Research Institute for System Studies of RAS, Moscow

Abstract: We prove the finiteness of the set of square-free polynomials $f \in k[x]$ of odd degree distinct from 11 considered up to a natural equivalence relation for which the continued fraction expansion of the irrationality $\sqrt{f(x)}$ in $k((x))$ is periodic and the corresponding hyperelliptic field $k(x)(\sqrt f)$ contains an $S$-unit of degree 11. Moreover, it was proved for $k = \mathbb{Q}$ that there are no polynomials of odd degree distinct from 9 and 11 satisfying the conditions mentioned above.

Funding Agency Grant Number
Russian Science Foundation 16-11-10111


DOI: https://doi.org/10.31857/S086956520003431-7


English version:
Doklady Mathematics, 2018, 98:3, 641–645

Bibliographic databases:

Received: 26.12.2018

Linking options:
  • http://mi.mathnet.ru/eng/dan46857

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:9

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019