On Addition Formulae for Sigma Functions of Telescopic Curves

Abstract

A telescopic curve is a certain algebraic curve defined by m−1 equations in the affine space of dimension m, which can be a hyperelliptic curve and an (n,s) curve as a special case. We extend the addition formulae for sigma functions of (n,s) curves to those of telescopic curves. The expression of the prime form in terms of the derivative of the sigma function is also given.

Keywords

• sigma function
• tau function
• Schur function
• Riemann surface
• telescopic curve
• gap sequence