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

3 Scopus citations


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


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

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


Dive into the research topics of 'Meromorphic matrix trivializations of factors of automorphy over a Riemann surface'. Together they form a unique fingerprint.

Cite this