ON DEGENERATE SIGMA-FUNCTIONS IN GENUS 2
| Autor: | Dmitry Leykin, Julia Bernatska |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Rank (linear algebra) General Mathematics 010102 general mathematics Degenerate energy levels Field (mathematics) 01 natural sciences Inversion (discrete mathematics) Elliptic curve Genus (mathematics) 0103 physical sciences Elementary function 010307 mathematical physics 0101 mathematics Mathematics Meromorphic function |
| Zdroj: | Glasgow Mathematical Journal. 61:169-193 |
| ISSN: | 1469-509X 0017-0895 |
| DOI: | 10.1017/s0017089518000162 |
| Popis: | We obtain explicit expressions for genus 2 degenerate sigma-function in terms of genus 1 sigma-function and elementary functions as solutions of a system of linear partial differential equations satisfied by the sigma-function. By way of application, we derive a solution for a class of generalized Jacobi inversion problems on elliptic curves, a family of Schrödinger-type operators on a line with common spectrum consisting of a point and two segments, explicit construction of a field of three-periodic meromorphic functions. Generators of rank 3 lattice in ℂ2are given explicitly. |
| Databáze: | OpenAIRE |
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