Counting points of fixed degree and given height over function fields
نویسندگان
چکیده
منابع مشابه
Counting Points of Fixed Degree and given Height over Function Fields
Let k be a finite algebraic extension of the field of rational functions in one indeterminate over a finite field and let k denote an algebraic closure of k. We count points in projective space Pn−1(k) with given height and generating an extension of fixed degree d over k. If n > 2d + 3 we derive an asymptotic estimate for the number of such points as the height tends to infinity. As an applica...
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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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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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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2012
ISSN: 0024-6093
DOI: 10.1112/blms/bds087