Infinite products over visible lattice points
نویسندگان
چکیده
منابع مشابه
Visible Lattice Points in Random Walks
We consider the possible visits to visible points of a random walker moving up and right in the integer lattice (with probability α and 1 − α, respectively) and starting from the origin. We show that, almost surely, the asymptotic proportion of strings of k consecutive visible lattice points visited by such an α-random walk is a certain constant ck(α), which is actually an (explicitly calculabl...
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For a prime p and an absolutely irreducible modulo p polynomial f(U, V ) ∈ Z[U, V ] we obtain an asymptotic formulas for the number of solutions to the congruence f(x, y) ≡ a (mod p) in positive integers x 6 X, y 6 Y , with the additional condition gcd(x, y) = 1. Such solutions have a natural interpretation as solutions which are visible from the origin. These formulas are derived on average ov...
متن کاملDiiraction from Visible Lattice Points and Kth Power Free Integers
We prove that the set of visible points of any lattice of dimension n 2 has pure point diiraction spectrum, and we determine the diiraction spectrum explicitly. This settles previous speculation on the exact nature of the diirac-tion in this situation. Using similar methods we show the same result for the 1-dimensional set of kth-power-free integers with k 2. Of special interest is the fact tha...
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We prove that the set of visible points of any lattice of dimension n ≥ 2 has pure point diffraction spectrum, and we determine the diffraction spectrum explicitly. This settles previous speculation on the exact nature of the diffraction in this situation. Using similar methods we show the same result for the 1-dimensional set of kth-power-free integers with k ≥ 2. Of special interest is the fa...
متن کاملInfinite Products of Infinite Measures
Let (Xi, Bi, mi) (i ∈ N) be a sequence of Borel measure spaces. There is a Borel measure μ on ∏ i∈N Xi such that if Ki ⊆ Xi is compact for all i ∈ N and ∏ i∈N mi(Ki) converges then μ( ∏ i∈N Ki) = ∏ i∈N mi(Ki)
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1994
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171294000918