Commuting differential operators of rank 2 with rational coefficients

Abstract

In this paper we find new self-adjoint commuting operators of rank 2 with rational coefficients and prove that any elliptic and hyperelliptic curves of genus 2 are spectral curves of commuting operators with rational coefficients. Also the case when curves of genus 3 are spectral curves of commuting operators with rational coefficients is studied.

23 pages

References in corpus (3)

• Commuting ordinary differential operators with polynomial coefficients and automorphisms of the first Weyl algebra
• Commuting differential operators of rank 2 with polynomial coefficients
• Common eigenfunctions of commuting differential operators of rank 2

Cited by in corpus (1)

• Centralizers of Rank One in the First Weyl Algebra