Geodesic
Buchstaber Formal Group and Elliptic Functions of Small Levels
Matematičeskie zametki, Tome 102 (2017) no. 1, pp. 96-108.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: formal groups, additivity theorems, elliptic functions. 
@article{MZM_2017_102_1_a9,
     author = {A. V. Ustinov},
     title = {Buchstaber {Formal} {Group} and {Elliptic} {Functions} of {Small} {Levels}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {96--108},
     publisher = {mathdoc},
     volume = {102},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a9/}
}
TY  - JOUR
AU  - A. V. Ustinov
TI  - Buchstaber Formal Group and Elliptic Functions of Small Levels
JO  - Matematičeskie zametki
PY  - 2017
SP  - 96
EP  - 108
VL  - 102
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a9/
LA  - ru
ID  - MZM_2017_102_1_a9
ER  - 
%0 Journal Article
%A A. V. Ustinov
%T Buchstaber Formal Group and Elliptic Functions of Small Levels
%J Matematičeskie zametki
%D 2017
%P 96-108
%V 102
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a9/
%G ru
%F MZM_2017_102_1_a9
A. V. Ustinov. Buchstaber Formal Group and Elliptic Functions of Small Levels. Matematičeskie zametki, Tome 102 (2017) no. 1, pp. 96-108. http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a9/

[1] N. I. Akhiezer, Elementy teorii ellipticheskikh funktsii, Nauka, M., 1970 | MR | Zbl

[2] I. M. Krichever, “Ellipticheskie resheniya uravneniya Kadomtseva–Petviashvili i integriruemye sistemy chastits”, Funkts. analiz i ego pril., 14:4 (1980), 45–54 | MR | Zbl

[3] V. M. Bukhshtaber, “Funktsionalnye uravneniya, assotsiirovannye s teoremami slozheniya dlya ellipticheskikh funktsii, i dvuznachnye algebraicheskie gruppy”, UMN, 45:3 (273) (1990), 185–186 | MR | Zbl

[4] V. M. Buchstaber, T. E. Panov, Toric Topology, Math. Surveys Monogr., 204, Amer. Math. Soc., Providence, RI, 2015 | MR | Zbl

[5] F. Hirzebruch, T. Berger, R. Jung, Manifolds and Modular Forms, Bonn, 1994 http://hirzebruch.mpim-bonn.mpg.de/id/eprint/110

[6] J. B. von Oehsen, “Elliptic genera of level N and Jacobi polynomials”, Proc. Amer. Math. Soc., 122:1 (1994), 303–312 | MR | Zbl

[7] V. M. Bukhshtaber, E. Yu. Bunkova, “Universalnaya formalnaya gruppa, opredelyayuschaya ellipticheskuyu funktsiyu urovnya 3”, Chebyshevskii sb., 16:2 (2015), 66–78

[8] V. M. Bukhshtaber, A. V. Ustinov, “Koltsa koeffitsientov formalnykh grupp”, Matem. sb., 206:11 (2015), 19–60 | DOI | MR | Zbl

[9] E. Yu. Bunkova, V. M. Bukhshtaber, A. V. Ustinov, “Koltsa koeffitsientov formalnykh grupp Teita, zadayuschikh rody Krichevera”, Algebra, geometriya i teoriya chisel, Sbornik statei. K 75-letiyu so dnya rozhdeniya akademika Vladimira Petrovicha Platonova, Tr. MIAN, 292, MAIK, M., 2016, 43–68 | DOI | Zbl

[10] V. M. Bukhshtaber, E. Yu. Bunkova, “Formalnye gruppy Krichevera”, Funkts. analiz i ego pril., 45:2 (2011), 23–44 | DOI | MR | Zbl

[11] E. Yu. Bunkova, “Ellipticheskaya funktsiya urovnya $4$”, Sovremennye problemy matematiki, mekhaniki i matematicheskoi fiziki. II, Sbornik statei, Tr. MIAN, 294, MAIK, M., 2016, 216–229 | DOI

[12] Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, eds. M. Abramovits, I. Stigan, Nauka, M., 1979 | MR | Zbl