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Automorphic forms in half-spaces. (English) Zbl 0095.06402

Semin. Analytic Functions, Princeton, Vol. 2, 105-119 (1958).
In the theory of modular forms and functions the half-plane \(\operatorname{Im} z > 0\) plays an important role. In the classical generalizations of this theory, e. g. modular forms of higher degree, Hermitian forms, modular forms of Hilbert a generalized half-plane is introduced. The author introduced in a former paper [Am. J. Math. 79, 575–596 (1957; Zbl 0078.01205)] the concept of domain of positivity, as an introduction to the definition of a generalized upper half-plane. With these general notions all the classical concepts e. g. modular group, fundamental domain, cusp form, can be studied once more. The author announces a number of theorems, well known in the classical case. It would be interesting to compare these generalization with the methods of Godement and Shimura.
For the entire collection see Zbl 0094.27201.

MSC:

11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
11F55 Other groups and their modular and automorphic forms (several variables)