On addition theorems related to elliptic integrals
Malkhaz Bakuradze, Vladimir Vershinin

TL;DR
This paper derives explicit addition formulas for elliptic integrals involving quartic polynomials, connecting classical elliptic integral theory with complex elliptic genera and extending Euler's addition theorem.
Contribution
It introduces new explicit formulas for addition theorems of elliptic integrals associated with degree 4 polynomials, enhancing understanding of their algebraic and geometric properties.
Findings
Explicit addition formulas for elliptic integrals with quartic polynomials
Connections established between elliptic integrals and complex elliptic genera
Extension of Euler's addition theorem to broader classes of elliptic integrals
Abstract
This paper provides some explicit formulas related to addition theorems for elliptic integrals , where is the square root from a polynomial of degree 4. These integrals are related to complex elliptic genera and are motivated by Euler's addition theorem for elliptic integrals of the first kind.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Holomorphic and Operator Theory · Algebraic and Geometric Analysis
