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 language | American English |
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Article number | oam-10-47 |
Pages (from-to) | 785-828 |
Number of pages | 44 |
Journal | Operators and Matrices |
Volume | 10 |
Issue number | 4 |
DOIs | |
State | Published - 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