Meromorphic matrix trivializations of factors of automorphy over a Riemann surface

Joseph A. Ball, Kevin F. Clancey, Victor Vinnikov

Research output: Contribution to journalArticlepeer-review

Abstract

It is a consequence of the Jacobi Inversion Theorem that a line bundle over a Riemann surface M of genus g has a meromorphic section having at most g poles, or equivalently, the divisor class of a divisor over M contains a divisor having at most g poles (counting multiplicities). We explore various analogues of these ideas for vector bundles and associated matrix divisors over M. The most explicit results are for the genus 1 case. We also review and improve earlier results concerning the construction of automorphic or relatively automorphic meromorphic matrix functions having a prescribed null/pole structure.

Original languageAmerican English
Article numberoam-10-47
Pages (from-to)785-828
Number of pages44
JournalOperators and Matrices
Volume10
Issue number4
DOIs
StatePublished - 1 Dec 2016

Keywords

  • Abel-Jacobi map
  • Factor of automorphy
  • Holomorphic vector bundle
  • Theta functions
  • Transfer-function realization
  • Zero/pole interpolation problems

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory

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