Geodesic
On Addition Theorems Related to Elliptic Integrals
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 29-39.

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We present formulas for the components of the Buchstaber formal group law and its exponent over $\mathbb Q[p_1,p_2,p_3,p_4]$. This leads to an addition theorem for the general elliptic integral $\int _0^x dt/R(t)$ with $R(t)=\sqrt {1+p_1t+p_2t^2+p_3t^3+p_4t^4}$. The study is motivated by Euler's addition theorem for elliptic integrals of the first kind.
Keywords: addition theorem, formal group law.
Mots-clés : complex elliptic genus 
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Malkhaz Bakuradze; Vladimir V. Vershinin. On Addition Theorems Related to Elliptic Integrals. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 29-39. http://geodesic.mathdoc.fr/item/TM_2019_305_a1/

[1] M. Bakuradze, “The formal group laws of Buchstaber, Krichever, and Nadiradze coincide”, Russ. Math. Surv., 68:3 (2013), 571–573 | DOI | DOI | MR | Zbl

[2] M. Bakuradze, “On the Buchstaber formal group law and some related genera”, Proc. Steklov Inst. Math., 286, 2014, 1–15 | DOI | DOI | MR | Zbl

[3] Bakuradze M., “Computing the Krichever genus”, J. Homotopy Relat. Struct., 9:1 (2014), 85–93 | DOI | MR | Zbl

[4] V. M. Buhštaber, “The Chern–Dold character in cobordisms. I”, Math. USSR, Sb., 12:4 (1970), 573–594 | DOI | MR | Zbl

[5] V. M. Bukhshtaber, “Functional equations associated with addition theorems for elliptic functions and two-valued algebraic groups”, Russ. Math. Surv., 45:3 (1990), 213–215 | DOI | MR | Zbl

[6] V. M. Buchstaber, “Complex cobordism and formal groups”, Russ. Math. Surv., 67:5 (2012), 891–950 | DOI | DOI | MR | Zbl

[7] V. M. Buchstaber and E. Yu. Bunkova, “Krichever formal groups”, Funct. Anal. Appl., 45:2 (2011), 99–116 | DOI | DOI | MR | Zbl

[8] Buchstaber V.M., Panov T.E., Toric topology, Math. Surv. Monogr., 204, Amer. Math. Soc., Providence, RI, 2015 | DOI | MR | Zbl

[9] V. M. Buchstaber and A. V. Ustinov, “Coefficient rings of formal group laws”, Sb. Math., 206:11 (2015), 1524–1563 | DOI | DOI | MR | Zbl

[10] Höhn G., Komplexe elliptische Geschlechter und $S^1$-äquivariante Kobordismustheorie, Diplomarbeit, Bonn Univ., Bonn, 1991; arXiv: math/0405232 [math.AT] | Zbl

[11] I. M. Krichever, “Generalized elliptic genera and Baker–Akhiezer functions”, Math. Notes, 47:2 (1990), 132–142 | DOI | MR | Zbl

[12] S. P. Novikov, “The methods of algebraic topology from the viewpoint of cobordism theory”, Math. USSR, Izv., 1:4 (1967), 827–913 | DOI | MR | Zbl

[13] Ochanine S., “Sur les genres multiplicatifs définis par des intégrales elliptiques”, Topology, 26:2 (1987), 143–151 | DOI | MR | Zbl

[14] Quillen D., “On the formal group laws of unoriented and complex cobordism theory”, Bull. Amer. Math. Soc., 75 (1969), 1293–1298 | DOI | MR | Zbl

[15] Schreieder S., “Dualization invariance and a new complex elliptic genus”, J. reine angew. Math., 692 (2014), 77–108 ; arXiv: 1109.5394v3 [math.AT] | MR | Zbl

[16] Whittaker E.T., Watson G.N., A course of modern analysis: An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions, Univ. Press, Cambridge, 1927 | MR | Zbl