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2008 Resolution of Degree $\leq 6$ Algebraic Equations by Genus Two Theta Constants
Angel Zhivkov
J. Geom. Symmetry Phys. 11: 77-93 (2008). DOI: 10.7546/jgsp-11-2008-77-93


We adjoin complete first kind Abelian integrals of genus two to resolve the general sextic equation $c_0 z^6 + c_1 z^5 + \cdots + c_6 = 0$ with simple zeros by genus two theta constants (Thetanullwerten). Using the same formulas, we also resolve each algebraic equation of degree five, four or three. It is shown that the monodromy group of a sextic is isomorphic to the second congruence sub-group $\Gamma (2)$ of the symplectic group ${\rm Sp}_4 ({\mathbb Z})$.


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Angel Zhivkov. "Resolution of Degree $\leq 6$ Algebraic Equations by Genus Two Theta Constants." J. Geom. Symmetry Phys. 11 77 - 93, 2008.


Published: 2008
First available in Project Euclid: 24 May 2017

zbMATH: 1162.14031
MathSciNet: MR243399
Digital Object Identifier: 10.7546/jgsp-11-2008-77-93

Rights: Copyright © 2008 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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