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Automorphic pseudodifferential operators, Poincaré series and Eisenstein series

Published online by Cambridge University Press:  17 April 2009

Min Ho Lee
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, United States of America e-mail: [email protected]
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Abstract

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We construct Poincaré series and Eisenstein series for automorphic pseudodifferential operators, and show that the space of automorphic pseudodifferential operators associated to cusp forms is generated by Poincaré series. We also obtain explicit formulas for such Poincaré series and Eisenstein series.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Cohen, P., Manin, Y. and Zagier, D., ‘Automorphic pseudodifferential operators’, Progr. Nonlinear Differential Equations Appl. 26 (1995), 1747.Google Scholar
[2]Dickey, L., Soliton equations and Hamiltonian systems (World Scientific, Singapore, 1991).CrossRefGoogle Scholar
[3]Miyake, T., Modular forms (Springer-Verlag, Berlin, Heidelberg, New York, 1989).CrossRefGoogle Scholar
[4]Takhtajan, L., ‘Modular forms as τ-functions for certain integrable reductions of the Yang-Mills equations’, in Progress in Math. 115 (Birkhäuser, Boston, 1993), pp. 115129.Google Scholar
[5]Zagier, D., ‘Modular forms and differential operators’, Proc. Indian Acad. Sci. Math. Sci. 104 (1994), 5775.CrossRefGoogle Scholar