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ON DEGENERATE SIGMA-FUNCTIONS IN GENUS 2

Published online by Cambridge University Press:  25 June 2018

JULIA BERNATSKA
Affiliation:
National University of Kyiv-Mohyla Academy, Kyiv 04655, Ukraine e-mails: [email protected], [email protected]
DMITRY LEYKIN
Affiliation:
NASU Institute of Magnetism, Kyiv 03142, Ukraine e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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