HILBERT MODULAR PSEUDODIFFERENTIAL OPERATORS OF MIXED WEIGHT

[摘要] 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

[学科分类] 数学（综合）

[关键词] Hilbert modular forms;pseudodifferential operators;automorphic forms