Uniformly counting points of bounded height
نویسندگان
چکیده
منابع مشابه
Counting Primitive Points of Bounded Height
Let k be a number field and K a finite extension of k. We count points of bounded height in projective space over the field K generating the extension K/k. As the height gets large we derive asymptotic estimates with a particularly good error term respecting the extension K/k. In a future paper we will use these results to get asymptotic estimates for the number of points of fixed degree over k...
متن کاملCounting Points of Fixed Degree and Bounded Height
We consider the set of points in projective n-space that generate an extension of degree e over given number field k, and deduce an asymptotic formula for the number of such points of absolute height at most X, as X tends to infinity. We deduce a similar such formula with instead of the absolute height, a so-called adelic-Lipschitz height.
متن کاملNonlinear codes from points of bounded height
This paper generalizes Elkies’ construction of error-correcting nonlinear codes found in [N. Elkies, Excellent nonlinear codes from modular curves, in: Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing, STOC’01, Hersonissos, Crete, Greece, 2001, pp. 200–208]. The generalization produces a precise average code size over codes in the new construction. The result is a larger ...
متن کاملPoints of Bounded Height on Algebraic Varieties
Introduction 1 1. Heights on the projective space 3 1.1. Basic height function 3 1.2. Height function on the projective space 5 1.3. Behavior under maps 7 2. Heights on varieties 9 2.1. Divisors 9 2.2. Heights 13 3. Conjectures 19 3.1. Zeta functions and counting 19 3.2. Height zeta function 20 3.3. Results and methods 22 3.4. Examples 24 4. Compactifications of Semi-Simple Groups 26 4.1. A Con...
متن کاملCounting points of fixed degree and bounded height on linear varieties
We count points of fixed degree and bounded height on a linear projective variety defined over a number field k. If the dimension of the variety is large enough compared to the degree we derive asymptotic estimates as the height tends to infinity. This generalizes results of Thunder, Christensen and Gubler and special cases of results of Schmidt and Gao.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2004
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa111-3-5