How many rational points does a random curve have?
نویسندگان
چکیده
منابع مشابه
How Many Rational Points Does a Random Curve Have?
A large part of modern arithmetic geometry is dedicated to or motivated by the study of rational points on varieties. For an elliptic curve over Q, the set of rational points forms a finitely generated abelian group. The ranks of these groups, when ranging over all elliptic curves, are conjectured to be evenly distributed between rank 0 and rank 1, with higher ranks being negligible. We will de...
متن کاملHow Many Random Points Can a Regular Curve Pass Through?
Suppose n points are scattered uniformly at random in the unit square [0, 1]. Question: How many of these points can possibly lie on some curves of length λ? Answer, proved here: OP (λ · √ n). We consider a general class of such questions; in each case, we are given a class Γ of curves in the square, and we ask: in a cloud of n uniform random points, how many can lie on some curve γ ∈ Γ? Classe...
متن کاملConnect-The-Dots: How many random points can a regular curve pass through?
Suppose n points are scattered uniformly at random in the unit square [0, 1]. Question: How many of these points can possibly lie on some curve of length λ? Answer, proved here: OP (λ · √ n). We consider a general class of such questions; in each case, we are given a class Γ of curves in the square, and we ask: in a cloud of n uniform random points, how many can lie on some curve γ ∈ Γ? Classes...
متن کاملHow Many Real Attractive Fixed Points Can A Polynomial Have?
We prove a complex polynomial of degree n has at most ⌈n/2⌉ attractive fixed points lying on a line. We also consider the general case.
متن کاملVarieties with Too Many Rational Points
We investigate Fano varieties defined over a number field, which contain subvarieties whose number of rational points of bounded height is comparable to the total number on the variety.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2013
ISSN: 0273-0979,1088-9485
DOI: 10.1090/s0273-0979-2013-01433-2