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The resultant on compact Riemann surfaces
KTH, Matemiska institutionen.
KTH, Matemiska institutionen.ORCID iD: 0000-0002-8422-6140
2009 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 286, no 1, 313-358 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer, 2009. Vol. 286, no 1, 313-358 p.
Keyword [en]
Resultant; meromorphic functions; Riemann surfaces
National Category
Mathematical Analysis Algebra and Logic
Identifiers
URN: urn:nbn:se:liu:diva-79622DOI: 10.1007/s00220-008-0622-2OAI: oai:DiVA.org:liu-79622DiVA: diva2:577309
Available from: 2012-12-14 Created: 2012-08-11 Last updated: 2017-12-06

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Tkachev, Vladimir

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