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Формальная группа Бухштабера и эллиптические функции малых уровней
Математические заметки. 2017. Т. 102. № 1. С. 96–108.
Ustinov A.
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.
Prokofev V., Zabrodin A., Mathematical Physics Analysis and Geometry 2023 Vol. 26 Article 20
We study elliptic solutions of the recently introduced Toda lattice with the constraint of type B and derive equations of motion for their poles. The dynamics of poles is given by the deformed Ruijsenaars-Schneider system. We find its commutation representation in the form of the Manakov triple and study properties of the spectral curve. By ...
Added: December 25, 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., Buchstaber V. M., Бунькова Е. Ю., Труды Математического института им. В.А. Стеклова РАН 2016 Т. 292 С. 43–68
The paper is devoted to problems at the intersection of formal group theory, the theory of Hirzebruch genera, and the theory of elliptic functions. In the focus of our interest are Tate formal groups corresponding to the general five-parametric model of the elliptic curve as well as formal groups corresponding to the general four-parametric Krichever ...
Added: October 7, 2025
Zabrodin A., Vadim Prokofev, Functional Analysis and Its Applications 2024 Vol. 58 No. 3 P. 289–298
Some identities that involve the elliptic version of the Cauchy matrices are presented
and proved. They include the determinant formula, the formula for the inverse matrix, the matrix
product identity and the factorization formula. ...
Added: November 28, 2024
Черных Г. С., Математические заметки 2023 Т. 113 № 6 С. 918–928
We describe the structure of the coefficient ring W(pt)=Ω^W of the c_1-spherical bordism theory for an arbitrary SU-bilinear multiplication. We prove that for any SU-bilinear multiplication the formal group of the theory W∗ is Landweber exact. Also we show that after inverting the set P of Fermat primes there exists a complex orientation of the localized theory W[P^(−1)] such that the coefficients of the corresponding formal ...
Added: October 28, 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
Prokofev V., Zabrodin A., Mathematical Physics Analysis and Geometry 2023 Vol. 26 No. 3 Article 20
We study elliptic solutions of the recently introduced Toda lattice with the constraint of type B and derive equations of motion for their poles. The dynamics of poles is given by the deformed Ruijsenaars-Schneider system. We find its commutation representation in the form of the Manakov triple and study properties of the spectral curve. By ...
Added: December 4, 2023
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
Шагай М. А., Флегонтов А. В., В кн.: Некоторые актуальные проблемы современной математики и математического образования. Материалы научной конференции "Герценовские чтения - 2022".: СПб.: РГПУ им. А.И. Герцена, 2022.
This article deals with classes of equations - the Weierstrass orbit, the tangent orbit, and the elliptic integral orbit, - whose solutions have a special structure. Through a finite set of special functions, all solutions are constructed by the method of differential "puzzles" after applying the algorithmic direct method. ...
Added: February 6, 2023
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
Ustinov A., Быковский В. А., Функциональный анализ и его приложения 2019 Т. 53 № 3 С. 79–83
В работе уточняется результат Зелевинского и Фомина (2002) о лорановости последовательностей Сомос-4 и Сомос-5 ...
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
Vostokov S. V., Афанасьева С. С., Bondarko M. V. et al., Vestnik St. Petersburg University: Mathematics 2017 Vol. 50 No. 3 P. 242–264
—This is a survey of results obtained by members of the St. Petersburg school of local number theory headed by S.V. Vostokov during the past decades. All these results hardly fit into the title of the paper, since they involve a large circle of ideas, which are applied to an even larger class of problems ...
Added: April 19, 2021
A. Levin, M. Olshanetsky, A. Zotov, Journal of Mathematical Physics 2020 Vol. 61 P. 103504
We introduce an odd supersymmetric version of the Kronecker elliptic function. It satisfies the genus one Fay identity and supersymmetric version of the heat equation. As an application, we construct odd supersymmetric extensions of the elliptic R-matrices, which satisfy the classical and the associative Yang–Baxter equations. ...
Added: November 10, 2020
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
A. Levin, M. Olshanetsy, A. Zotov, / Series arXiv:1910.05712 "math-ph". 2019.
We study a general ansatz for an odd supersymmetric version of the Kronecker elliptic function, which satisfies the genus one Fay identity. The obtained result is used for construction of the odd supersymmetric analogue for the classical and quantum elliptic R -matrices. They are shown to satisfy the classical Yang-Baxter equation and the associative Yang-Baxter ...
Added: November 1, 2019