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HILBERT MODULAR PSEUDODIFFERENTIAL OPERATORS OF MIXED WEIGHT

Published online by Cambridge University Press:  04 July 2003

Min Ho Lee  and
Hyo Chul Myung
Min Ho Lee
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, USA ([email protected])
Hyo Chul Myung
Affiliation:
Korea Institute for Advanced Study, 207-43 Chunryangri-dong, Dongdaemoon-ku, Seoul 130-012, Korea ([email protected])
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Abstract

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We introduce an action of a discrete subgroup $\varGamma$ of $SL(2,\mathbb{R})^n$ on the space of pseudodifferential operators of $n$ variables, and construct a map from the space of Hilbert modular forms for $\varGamma$ to the space of pseudodifferential operators invariant under such a $\varGamma$-action, which is a lifting of the symbol map of pseudodifferential operators. We also obtain a necessary and sufficient condition for a certain type of pseudodifferential operator to be $\varGamma$-invariant.

AMS 2000 Mathematics subject classification: Primary 11F41; 35S05

Keywords

Hilbert modular formspseudodifferential operatorsautomorphic forms
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 2 , June 2003 , pp. 269 - 277
Copyright
Copyright © Edinburgh Mathematical Society 2003