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Automorphic pseudodifferential operators, Poincaré series and Eisenstein series
Published online by Cambridge University Press: 17 April 2009
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.
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- Research Article
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- Copyright © Australian Mathematical Society 1999
References
[1]Cohen, P., Manin, Y. and Zagier, D., ‘Automorphic pseudodifferential operators’, Progr. Nonlinear Differential Equations Appl. 26 (1995), 17–47.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. 115–129.Google Scholar
[5]Zagier, D., ‘Modular forms and differential operators’, Proc. Indian Acad. Sci. Math. Sci. 104 (1994), 57–75.CrossRefGoogle Scholar