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О лорановости последовательностей Сомос-4 и Сомос-5
Функциональный анализ и его приложения. 2019. Т. 53. № 3. С. 79–83.
Ustinov A., Быковский В. А.
Быковский В. А., Ustinov A., Доклады Академии наук 2016 Т. 471 № 1 С. 7–10
A general formula for elements of dual Somos-4 sequences is obtained. A sufficient condition for the integerness of such sequences is proposed. ...
Added: October 12, 2025
Быковский В. А., Романов М. А., Ustinov A., Чебышевский сборник 2021 Т. 22 № 1 С. 118–132
Since the seminal note published by M. Somos in 1989, a great deal of attention of specialists in number theory and adjacent areas are attracted by nonlinear sequences that satisfy a quadratic recurrence relation. At the same time, special attention is paid to the construction of Somos integer sequences and their Laurent property with respect to ...
Added: October 12, 2025
Buchstaber V. M., Ustinov A., Математический сборник 2015 Т. 206 № 11 С. 19–60
We describe the coefficient rings of universal formal group laws which arise in algebraic geometry, algebraic topology and their application to mathematical physics. We also describe the homomorphisms of these coefficient rings coming from reductions of one formal group law to another. The proofs are based on the number-theoretic properties of binomial coefficients. ...
Added: October 9, 2025
Ustinov A., Математические заметки 2017 Т. 102 № 1 С. 96–108
In the paper, we suggest a method for finding relations concerning series defining the Buchstaber formal group. This method is applied to the cases in which the exponent of the group is an elliptic function of level n=2,3, and 4. An algebraic relation for the series defining the universal Buchstaber formal group is also proved. ...
Added: October 7, 2025
A. V. Ustinov, Mathematical Notes, USA 2024 Vol. 115 No. 3 P. 405–413
We prove the periodicity of finite rank Somos sequences modulo m. As an application, we prove the periodicity of the Somos-(6) (mod m) sequence. ...
Added: July 6, 2024
Ustinov A., Математические заметки 2024 Т. 115 № 3 С. 439–449
We prove the periodicity of finite rank Somos sequences modulo m. As an application, we prove the periodicity of the Somos-(6) (mod m) sequence. ...
Added: April 16, 2024
Ustinov A., Квант 2023 № 9 С. 11–19
The article is devoted to Somos sequences and their properties. ...
Added: March 24, 2024
Ustinov A., Квант 2023 № 8 С. 8–14
The article is devoted to Somos sequences and their properties. ...
Added: March 24, 2024
Illarionov A., Известия РАН. Серия математическая 2023 Т. 87 № 6 С. 76–102
Выводятся формулы для последовательностей комплексных чисел, удовлетворяющие функциональным соотношениям билинейного типа. Полученные результаты используются для описания всех целых 1-периодических функций $f,g: C→C$, удовлетворяющих вместе с некоторыми $ϕ_j,ψ_j:C\to C$ разложению $f(x+y)g(x−y)=ϕ_1(x)ψ_1(y)+⋯+ϕ_4(x)ψ_4(y)$. ...
Added: January 16, 2024
Illarionov A., Математические заметки 2020 Т. 107 № 1 С. 80–92
Решается функциональное уравнение, связанное с теоремами сложения и эллиптическими функциями ...
Added: November 15, 2023
Ustinov A., Математические заметки 2021 Т. 110 № 3 С. 478–480
О последовательностях Сомос-4 и Сомос-5 ...
Added: November 25, 2021
Ustinov A., Труды Математического института им. В.А. Стеклова РАН 2019 Т. 305 С. 330–343
Предлагается элементарный подход (не использующий теорию эллиптических функций) к доказательству основных свойств последовательности Сомос-4. ...
Added: November 25, 2021
Ustinov A., Математические заметки 2019 Т. 105 № 6 С. 899–910
В настоящей работе дается полное описание формальных групп Бухштабера
F(u,v)=\frac{u^2 A(v)-v^2 A(u)}{uB(v)-vB(u)},
для которых ряды A(x) и B(x) связаны соотношением A(x)ℓ=B(x)m. Получено новое семейство формальных групп Бухштабера, зависящее от двух алгебраически независимых параметров.
Библиография: 12 названий. ...
Added: November 25, 2021
Mosharev P., Кечкин О. В., Moscow University Physics Bulletin 2020 Vol. 75 No. 5 P. 427–433
An exact expression is obtained for harmonic fields in Maxwell electrodynamics with dilatons in terms of elliptic Jacobi functions and elliptic Legendre integrals. The case of centrally symmetric fields is considered individually and effective charges of all three types, that is, electric, magnetic, and dilaton charges, are calculated. An expression is given for the generalized ...
Added: September 28, 2021
Semenov-Tian-Shansky K. M., Поляков М. В., Смирнов А. О. et al., Теоретическая и математическая физика 2019 Т. 200 № 2 С. 290–309
Leading logarithms in massless nonrenormalizable effective field theories can be computed using nonlinear
recurrence relations. These recurrence relations follow from the fundamental requirements of unitarity,
analyticity, and crossing symmetry of scattering amplitudes and generalize the renormalization group
technique to the case of nonrenormalizable effective field theories. We review the existing exact solutions
of nonlinear recurrence relations relevant for field ...
Added: September 29, 2020
Takebe T., Tokyo: Nippon Hyoron Sha, 2019.
The theory of elliptic integrals and elliptic functions, which were driving force of mathematics in the eighteenth and nineteents centuries, are not only beautiful but have many applications in mathematics and physics. This simple reader-friendly book, based on the lectures at the Faculty of Mathematics, HSE, explains such theory and applications in original way. ...
Added: October 25, 2019