منابع مشابه
Revisiting the Siegel Upper Half Plane I
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...
متن کاملThe p-adic upper half plane
The p-adic upper half plane X is a rigid analytic variety over a p-adic field K, on which the group GL2(K) acts, that Mumford introduced (as a formal scheme) as part of his efforts to generalize Tate’s p-adic uniformization of elliptic curves to curves of higher genus. The Cp–valued points of X are just P(Cp)−P(K), with GL2(K) acting by linear fractional transformations. Mumford showed that the...
متن کاملThe Algebraist ' S Upper Half - Plane
Introduction. The purpose of this article is to introduce the general mathematical community to some recent developments in algebraic geometry and nonarchimedean analysis. Let r = p,p a rational prime. Then these developments center around the beginnings of an "arithmetic" theory of the polynomial ring ¥r[T] over the finite field of r elements. The goal of this theory is to use nonarchimedean a...
متن کاملRevisiting the Siegel Upper Half Plane Ii
In this paper we study the automorphisms of Siegel upper half plane of complex dimension 3. We give the normal forms and classify the set of fixed points of such transformations. 1
متن کاملAn Introduction to Upper Half Plane Polynomials
For example, x1 + · · · + xd ∈ Ud (C). This follows from the fact that the upper half plane is a cone, so if σ1, . . . , σd are in the upper half plane then so is their sum. Another example is x1x2 − 1. If σ1 and σ2 are in the upper half plane then σ1σ2 ∈ C \ (0,∞), so σ1σ2 − 1 is not zero. U1 (C) is easily described. It is all polynomials in one variable whose roots are either real, or lie in ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1980
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1980-14751-5