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 Tr. Mat. Inst. Steklova, 2019, Volume 305, Pages 29–39 (Mi tm3991)

On Addition Theorems Related to Elliptic Integrals

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

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.

 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.

DOI: https://doi.org/10.4213/tm3991

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English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 305, 22–32

Bibliographic databases:

UDC: 512.54+515.1
MSC: 33E05, 55N22
Revised: January 18, 2019
Accepted: March 2, 2019

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, Tr. 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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