Мақаланы E-mail арқылы жіберу Proper cyclic symmetries of multidimensional continued fractions
- Авторлар: Tlyustangelov I.A.1,2
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Мекемелер:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Moscow Center for Fundamental and Applied Mathematics
- Шығарылым: Том 213, № 9 (2022)
- Беттер: 138-166
- Бөлім: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133469
- DOI: https://doi.org/10.4213/sm9690
- ID: 133469
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Аннотация
We show that palindromic continued fractions exist in an arbitrary dimension. For dimension $n=4$ we also prove a criterion for an algebraic continued fraction to have a proper cyclic palindromic symmetry. Klein polyhedra are considered as multidimensional generalizations of continued fractions. Bibliography: 11 titles.
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Авторлар туралы
Ibragim Tlyustangelov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Moscow Center for Fundamental and Applied Mathematics
Email: ibragim-tls@yandex.ru
Candidate of physico-mathematical sciences, no status
Әдебиет тізімі
- F. Klein, “Ueber eine geometrische Auffassung der gewöhnlichen Kettenbruchentwicklung”, Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl., 1895 (1895), 357–359
- J.-L. Lagrange, “Additions au memoire sur la resolution des equations numeriques”, Mem. Acad. Roy. Sci. et Belles-lettres de Berlin, 24 (1770), 581–652
- А. Я. Хинчин, Цепные дроби, 4-е изд., Наука, М., 1978, 112 с.
- O. N. German, I. A. Tlyustangelov, “Palindromes and periodic continued fractions”, Mosc. J. Comb. Number Theory, 6:2-3 (2016), 233–252
- О. Н. Герман, И. А. Тлюстангелов, “Симметрии двумерной цепной дроби”, Изв. РАН. Сер. матем., 85:4 (2021), 53–68
- Е. И. Коркина, “Двумерные цепные дроби. Самые простые примеры”, Особенности гладких отображений с дополнительными структурами, Сборник статей, Тр. МИАН, 209, Наука, Физматлит, М., 1995, 143–166
- E. Galois, “Analyse algebrique. Demonstration d'un theorème sur les fractions continues periodiques”, Ann. Math. Pures Appl. [Ann. Gergonne], 19 (1828/29), 294–301
- A.-M. Legendre, Theorie des nombres, v. 1, 2, 3 ed., Firmin Didot Frères, Libraires, Paris, 1830, xxiv+396 pp., xv+463 pp.
- O. Perron, Die Lehre von den Kettenbrüchen, v. 1, Elementare Kettenbrüche, 3. Aufl., B. G. Teubner Verlagsgesellschaft, Stuttgart, 1954, vi+194 pp.
- M. Kraitchik, Theorie des nombres, v. 2, Analyse indeterminee du second degre et factorisation, Gauthier-Villars, Paris, 1926, iv+252 pp.
- D. H. Lehmer, “A note on trigonometric algebraic numbers”, Amer. Math. Monthly, 40:3 (1933), 165–166
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