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О формальных группах Бухштабера специального вида
Математические заметки. 2019. Т. 105. № 6. С. 899–910.
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
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
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
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., 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
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