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ON DEGENERATE SIGMA-FUNCTIONS IN GENUS 2

Part of: Holomorphic functions of several complex variables Other special functions Representations of solutions

Published online by Cambridge University Press:  25 June 2018

JULIA BERNATSKA Open the ORCID record for JULIA BERNATSKA [Opens in a new window]  and
DMITRY LEYKIN
JULIA BERNATSKA
Affiliation:
National University of Kyiv-Mohyla Academy, Kyiv 04655, Ukraine e-mails: bernatska.julia@ukma.edu.ua, jbernatska@gmail.com
DMITRY LEYKIN
Affiliation:
NASU Institute of Magnetism, Kyiv 03142, Ukraine e-mail: dmitry.leykin@gmail.com
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Abstract

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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 ℂ2 are given explicitly.

MSC classification

Secondary: 32A20: Meromorphic functions 33E05: Elliptic functions and integrals 35C05: Solutions in closed form

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 1 , January 2019 , pp. 169 - 193
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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