Jacobian nullwerte and algebraic equations. (English) Zbl 1054.14041

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.


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


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