Extended automorphic forms on the upper half plane
نویسندگان
چکیده
منابع مشابه
Extended automorphic forms on the upper half plane
A variant of Hadamard’s notion of partie finie is applied to the theory of automorphic functions on arithmetic quotients of the upper half-plane. As a consequence, conceptually simple proofs of the volume formula and the Maass-Selberg relations are given. This technique interprets Zagier’s idea of renormalization (Jour. Fac. Sci. Univ. Tokyo 28 (1982), 415–437) so that it can be generalized eas...
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Many computations in the harmonic analysis of automorphic forms, especially concerning Eisenstein series, or, even worse, trace formulas, expose one to the danger that a naive formal approach leads to incorrect manipulation of expressions whose convergence is fragile or even volatile. At the same time it is often clear that some improved formalism can be correct, and may be more intelligible th...
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In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...
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In this paper, rstly, we obtain some inequalities which estimates complex polynomials on the circles.Then, we use these estimates and a Moebius transformation to obtain the dual of this estimates forthe lines in upper half-plane. Finally, for an increasing weight on the upper half-plane withcertain properties and holomorphic functions f on the upper half-plane we obtain an equivalentrepresenta...
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In the first part of the paper we show that the Busemann 1-compactification of the Siegel upper half plane of rank n: SHn = Sp(n, R)/Kn is the compactification as a bounded domain. In the second part of the paper we study certain properties of discrete groups Γ of biholomorphisms of SHn. We show that the set of accumulation points of the orbit Γ(Z) on the Shilov boundary of SHn is independent o...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 1993
ISSN: 0025-5831,1432-1807
DOI: 10.1007/bf01445135