Faculty Publications

Hecke Operators On Linear Ordinary Differential Equations

Document Type

Article

Keywords

Automorphic forms, Hecke operators, Ordinary differential equations

Journal/Book/Conference Title

Acta Applicandae Mathematicae

Volume

59

Issue

2

First Page

203

Abstract

We construct Hecke operators acting on the space of certain linear ordinary differential equations, and describe a Hermitian inner product on the space of such differential equations. We also determine the adjoint of the Hecke operator with respect to this inner product, and prove that the space of ordinary differential equations associated to an automorphic form for a certain discrete subgroup of SL(2, ℝ) has a basis consisting of common eigenvectors of a class of Hecke operators.

Department

Department of Mathematics

Original Publication Date

1-1-1999

DOI of published version

10.1023/a:1006396824182

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