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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
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.
Received: September 5, 2018 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, Trudy Mat. Inst. Steklova, 305, Steklov Math. Inst. RAS, Moscow, 2019, 29–39; Proc. Steklov Inst. Math., 305 (2019), 22–32
Linking options:
https://www.mathnet.ru/eng/tm3991https://doi.org/10.4213/tm3991 https://www.mathnet.ru/eng/tm/v305/p29
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