Algebraic S-integers of fixed degree and bounded height
نویسندگان
چکیده
منابع مشابه
Integral Points of Fixed Degree and Bounded Height
By Northcott’s Theorem there are only finitely many algebraic points in affine n-space of fixed degree e over a given number field and of height at most X. Finding the asymptotics for these cardinalities as X becomes large is a long standing problem which is solved only for e = 1 by Schanuel, for n = 1 by Masser and Vaaler, and for n “large enough” by Schmidt, Gao, and the author. In this paper...
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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 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...
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We describe an algorithm which, given a number field K and a bound B, finds all the elements of K having relative height at most B. Two lists of numbers are computed: one consisting of elements x ∈ K for which it is known with certainty that HK(x) ≤ B, and one containing elements x such that |HK(x)− B| < θ for a tolerance θ chosen by the user. We show that every element of K whose height is at ...
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: 2015
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa167-1-4