Pair correlation of sums of rationals with bounded height
نویسندگان
چکیده
منابع مشابه
Approximating reals by sums of two rationals
We generalize Dirichlet's diophantine approximation theorem to approximating any real number α by a sum of two rational numbers a 1 q 1 + a 2 q 2 with denominators 1 ≤ q1, q2 ≤ N. This turns out to be related to the congruence equation problem xy ≡ c (mod q) with 1 ≤ x, y ≤ q 1/2+ǫ .
متن کاملApproximating Reals by Sums of Rationals
Moreover, the above upper bound 1/(qN) is best possible apart from a scalar multiple when one considers the golden ratio θ = ( √ 5 − 1)/2 (for a proof, one may use Theorem 181 and bottom of page 162 in [2] on certain properties of continued fractions). During his work in [1], the author accidentally stumbled across the following analogous question: Question 1. For any real θ and any integer N ≥...
متن کاملSums of Two Squares – Pair Correlation & Distribution in Short Intervals
In this work we show that based on a conjecture for the pair correlation of integers representable as sums of two squares, which was first suggested by Connors and Keating and reformulated here, the second moment of the distribution of the number of representable integers in short intervals is Poissonian, where “short” means of length comparable to the mean spacing between sums of two squares. ...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2010
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle.2010.027