Counting integral points in certain homogeneous spaces
نویسندگان
چکیده
منابع مشابه
Counting orbits of integral points in families of affine homogeneous varieties and diagonal flows
In this paper, we study the distribution of integral points on parametric families of affine homogeneous varieties. By the work of Borel and Harish-Chandra, the set of integral points on each such variety consists of finitely many orbits of arithmetic groups, and we establish an asymptotic formula (on average) for the number of the orbits indexed by their Siegel weights. Our arguments use the e...
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Given a convex rational polytope b = x ∈ n+ Ax= b , we consider the function b → f b , which counts the nonnegative integral points of b . A closed form expression of its -transform z → z is easily obtained so that f b can be computed as the inverse -transform of . We then provide two variants of an inversion algorithm. As a by-product, one of the algorithms provides the Ehrhart polynomial of a...
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Let X be an algebraic variety over a finite field Fq, homogeneous under a linear algebraic group. We show that there exists an integer N such that for any positive integer n in a fixed residue class mod N , the number of rational points of X over Fqn is a polynomial function of q with integer coefficients. Moreover, the shifted polynomials, where q is formally replaced with q +1, have non-negat...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2016
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2015.09.043