Resolution of degree ${\mathbf{\leq 6}}$ algebraic equations by genus two theta constants

Angle Zhivkov

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 14

MSC 2000

01A60 20th century
12D10 Polynomials: location of zeros (algebraic theorems)

Abstract
We adjoin complete first kind Abelian integrals of genus two to solve the general degree six algebraic equation $a_0 z^6 + a_1 z^5 + \cdots + a_6 = 0$ by genus two theta constants. Using the same formulas, later we resolve degree five, four and three algebraic equations. We study the monodromy group, which permutes the roots of degree six polynomials.

Keywords: roots of polynomials, theta constants