$p$-adic monomial equations and their perturbations

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In this paper, we describe the set of solutionsof the monomial equation $x^k=a$ over $\mathbb Q_p$. Moreover, asan application, we study some perturbations of the equation under consideration over the $p$-adic field.

作者简介

Farrukh Mukhamedov

United Arab Emirates University

Email: far75m@yandex.com
Doctor of physico-mathematical sciences, Professor

Otabek Khakimov

United Arab Emirates University

Email: hakimovo@mail.ru
Doctor of physico-mathematical sciences, Associate professor

参考

  1. A. Yu. Khrennikov, S. V. Kozyrev, W. A. Zuñiga-Galindo, Ultrametric pseudodifferential equations and applications, Encyclopedia Math. Appl., 168, Cambridge Univ. Press, Cambridge, 2018, xv+237 pp.
  2. S. Albeverio, R. Cianci, A. Yu. Khrennikov, “$p$-adic valued quantization”, $p$-Adic Numbers Ultrametric Anal. Appl., 1:2 (2009), 91–104
  3. V. Anashin, A. Khrennikov, Applied algebraic dynamics, De Gruyter Exp. Math., 49, Walter de Gruyter & Co., Berlin, 2009, xxiv+533 pp.
  4. B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, “On $p$-adic mathematical physics”, $p$-Adic Numbers Ultrametric Anal. Appl., 1:1 (2009), 1–17
  5. B. Dragovich, A Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, E. I. Zelenov, “$p$-adic mathematical physics: the first 30 years”, $p$-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121
  6. А. Ю. Хренников, Неархимедов анализ и его приложения, Физматлит, М., 2003, 216 с.
  7. B. C. Владимиров, И. В. Волович, Е. И. Зеленов, $p$-адический анализ и математическая физика, Наука, М., 1994, 352 с.
  8. З. И. Боревич, И. Р. Шафаревич, Теория чисел, 3-е доп. изд., Наука, М., 1985, 504 с.
  9. Ф. М. Мухамедов, Б. А. Омиров, М. Х. Сабуров, К. К. Масутова, “О разрешимости кубических уравнений в множестве целых $p$-адических чисел ($p>3$)”, Сиб. матем. журн., 54:3 (2013), 637–654
  10. F. Mukhamedov, M. Saburov, “On equation $x^q=a$ over $mathbb Q_p$”, J. Number Theory, 133:1 (2013), 55–58
  11. J. M. Casas, B. A. Omirov, U. A. Rozikov, “Solvability criteria for the equation $x^q = a$ in the field of $p$-adic numbers”, Bull. Malays. Math. Sci. Soc. (2), 37:3 (2014), 853–863
  12. F. Mukhamedov, “A dynamical system approach to phase transitions for $p$-adic Potts model on the Cayley tree of order two”, Rep. Math. Phys., 70:3 (2012), 385–406
  13. F. Mukhamedov, O. Khakimov, “Chaotic behavior of the $p$-adic Potts–Bethe mapping”, Discrete Contin. Dyn. Syst., 38:1 (2018), 231–245
  14. E. Yurova Axelsson, A. Khrennikov, “Generalization of Hensel's lemma: finding the roots of $p$-adic Lipschitz functions”, J. Number Theory, 158 (2016), 217–233
  15. Е. И. Юрова Аксельссон, А. Ю. Хренников, “Подкоординатное представление $p$-адических функций и обобщение леммы Гензеля”, Изв. РАН. Сер. матем., 82:3 (2018), 192–206
  16. F. Mukhamedov, “Recurrence equations over trees in a non-Archimedean context”, $p$-Adic Numbers Ultrametric Anal. Appl., 6:4 (2014), 310–317
  17. W. H. Schikhof, Ultrametric calculus. An introduction to $p$-adic analysis, Cambridge Stud. Adv. Math., 4, Cambridge Univ. Press, Cambridge, 1984, viii+306 pp.
  18. Н. Коблиц, $p$-адические числа, $p$-адический анализ и дзета-функции, Мир, М., 1982, 192 с.
  19. В. С. Анашин, А. Ю. Хренников, Е. И. Юрова, “Характеризация эргодических $p$-адических динамических систем в терминах базиса ван дер Пута”, Докл. РАН, 438:2 (2011), 151–153
  20. K. H. Rosen, Elementary number theory and its applications, 6th ed., Pearson, USA, 2011, 752 pp.
  21. M. A. Kh. Ahmad, Lingmin Liao, M. Saburov, “Periodic $p$-adic Gibbs measures of $q$-state Potts model on Cayley trees. I. The chaos implies the vastness of the set of $p$-adic Gibbs measures”, J. Stat. Phys., 171:6 (2018), 1000–1034
  22. F. Mukhamedov, “On the existence of generalized Gibbs measures for the one-dimensional $p$-adic countable state Potts model”, Избранные вопросы математической физики и $p$-адического анализа, Сборник статей, Тр. МИАН, 265, МАИК “Наука/Интерпериодика”, М., 2009, 177–188
  23. F. M. Mukhamedov, U. A. Rozikov, “On Gibbs measures of $p$-adic Potts model on the Cayley tree”, Indag. Math. (N. S.), 15:1 (2004), 85–99

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