Hilbert modular pseudodifferential operators (Q2731902)
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scientific article; zbMATH DE number 1626779
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hilbert modular pseudodifferential operators |
scientific article; zbMATH DE number 1626779 |
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Hilbert modular pseudodifferential operators (English)
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30 July 2001
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pseudo-differential operators
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automorphic forms of several variables
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Jacobi-like functions
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Hilbert modular forms
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\textit{P. B. Cohen, Yu. Manin} and \textit{D. Zagier} [Algebraic aspects of integrable systems, Prog. Nonlinear Differ. Equ. Appl. 26, 17--47 (1997; Zbl 1055.11514)] started a systematic treatment of pseudo-differential operators in the context of automorphic forms. In this paper under review, the author investigates certain generalizations of automorphic forms of several variables, namely to Jacobi-like functions and to Hilbert modular forms. Parts of the results are not true in this general context, because the Koecher effect does not hold for arbitrary discrete subgroups of \(\mathrm{SL}_2(\mathbb R)^n\).
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