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On the AF-algebra of a Hecke eigenform

Part of: Selfadjoint operator algebras Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  08 November 2011

Igor V. Nikolaev
Igor V. Nikolaev
Affiliation:
The Fields Institute for Mathematical Sciences, 222 College Street, Toronto, Ontario M5T 3J1, Canada (igor.v.nikolaev@gmail.com)
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Abstract

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An AF-algebra is assigned to each cusp form f of weight 2; we study properties of this operator algebra when f is a Hecke eigenform.

Keywords

modular formsfoliationsoperator algebras

MSC classification

Secondary: 11F03: Modular and automorphic functions 46L85: Noncommutative topology

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 1 , February 2012 , pp. 207 - 213
Copyright
Copyright © Edinburgh Mathematical Society 2011

References

1.Bauer, M., A characterization of uniquely ergodic interval exchange maps in terms of the Jacobi-Perron algorithm, Bol. Soc. Bras. Mat. 27 (1996), 109–128.CrossRefGoogle Scholar
2.Bernstein, L., The Jacobi-Perron algorithm, its theory and applications, Lecture Notes in Mathematics, Volume 207 (Springer, 1971).CrossRefGoogle Scholar
3.Borevich, Z. I. and Shafarevich, I. R., Number theory (Academic Press, New York, 1966).Google Scholar
4.Diamond, F. and Shurman, J., A first course in modular forms, Graduate Texts in Mathematics, Volume 228 (Springer, 2005).Google Scholar
5.Effros, E. G., Dimensions and C*-algebras, CBMS Regional Conference Series in Mathematics, Volume 46 (American Mathematical Society, Providence, RI, 1981).CrossRefGoogle Scholar
6.Hubbard, J. and Masur, H., Quadratic differentials and foliations, Acta Math. 142 (1979), 221–274.CrossRefGoogle Scholar
7.Perron, O., Grundlagen für eine Theorie des Jacobischen Kettenbruchalgorithmus, Math. Annalen 64 (1907), 1–76.CrossRefGoogle Scholar