The resultant on compact Riemann surfaces

Abstract

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.

44 pages

References in corpus (5)

• Conformal maps and dispersionless integrable hierarchies
• Integrable Structure of the Dirichlet Boundary Problem in Two Dimensions
• Laplacian Growth and Whitham Equations of Soliton Theory
• Integrable Structure of the Dirichlet Boundary Problem in Multiply-Connected Domains
• Ullemar's formula for the moment map, II

Cited by in corpus (8)

• New and Old Results in Resultant Theory
• Introduction to Integral Discriminants
• On the exponential transform of multi-sheeted algebraic domains
• Livsic-type Determinantal Representations and Hyperbolicity
• Resultant as Determinant of Koszul Complex
• On the exponential transform of lemniscates
• Tate tame symbol and the joint torsion of commuting operators
• Computing distances on Riemann surfaces