Hostname: page-component-599cfd5f84-jr95t Total loading time: 0 Render date: 2025-01-07T07:12:53.123Z Has data issue: false hasContentIssue false
  • English
  • Français

Automorphic pseudodifferential operators, Poincaré series and Eisenstein series

Published online by Cambridge University Press:  17 April 2009

Min Ho Lee
Min Ho Lee
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, United States of America e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 45 - 52
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), 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