Jacobian nullwerte and algebraic equations. (English) Zbl 1054.14041

Guàrdia, Jordi

J. Algebra 253, No. 1, 112-132 (2002).

Summary: We present two applications of Jacobian nullwerte, both related with the resolution of algebraic equations of any degree. We give a very simple expression of the roots of a polynomial of arbitrary degree in terms of derivatives of hyperelliptic theta functions. This expression can be understood as an explicit proof of Torelli’s theorem in the hyperelliptic case. We also give geometrical expressions of the discriminant of a polynomial. Both applications are based on a Jacobian version of Thomae’s formula.

MSC:

14H42	Theta functions and curves; Schottky problem
14C34	Torelli problem
14H40	Jacobians, Prym varieties
14H52	Elliptic curves

Keywords:

hyperelliptic theta functions; discriminant; Thomae’s formula

References:

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