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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 305, Pages 29–39
DOI: https://doi.org/10.4213/tm3991 (Mi tm3991) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On Addition Theorems Related to Elliptic Integrals

Malkhaz Bakuradzea, Vladimir V. Vershininbc

a Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, Chavchavadze Ave. 1, 0179 Tbilisi, Georgia
b Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, Case courrier 051, Place Eugène Bataillon, 34090 Montpellier, France
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090 Russia
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DOI: https://doi.org/10.4213/tm3991
Abstract: 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, complex elliptic genus, formal group law.
Funding agency Grant number
Centre National de la Recherche Scientifique 7736
Shota Rustaveli National Science Foundation 217-614
The work was supported by the CNRS PICS, grant no. 7736. The first author was also supported by the Shota Rustaveli National Science Foundation of Georgia, grant no. 217-614.
Received: September 5, 2018
Revised: January 18, 2019
Accepted: March 2, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 305, Pages 22–32
DOI: https://doi.org/10.1134/S0081543819030027
Bibliographic databases:
Document Type: Article
UDC: 512.54+515.1
MSC: 33E05, 55N22
Language: Russian
Citation: Malkhaz Bakuradze, Vladimir V. Vershinin, “On Addition Theorems Related to Elliptic Integrals”, Algebraic topology, combinatorics, and mathematical physics, Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 305, Steklov Math. Inst. RAS, Moscow, 2019, 29–39; Proc. Steklov Inst. Math., 305 (2019), 22–32
Citation in format AMSBIB
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\inbook Algebraic topology, combinatorics, and mathematical physics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday
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    • This publication is cited in the following 2 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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