SPHERICAL MEANS AND PINNED DISTANCE SETS
نویسندگان
چکیده
منابع مشابه
Spherical Means and Pinned Distance Sets
We use mixed norm estimates for the spherical averaging operator to obtain some results concerning pinned distance sets.
متن کاملSpherical two-distance sets
A set S of unit vectors in n−dimensional Euclidean space is called spherical two-distance set, if there are two numbers a and b so that the inner products of distinct vectors of S are either a or b. The largest cardinality g(n) of spherical two-distance sets does not exceed n(n+3)/2. This upper bound is known to be tight for n = 2, 6, 22. The set of midpoints of the edges of a regular simplex g...
متن کاملNew Bounds for Equiangular Lines and Spherical Two-Distance Sets
The set of points in a metric space is called an s-distance set if pairwise distances between these points admit only s distinct values. Two-distance spherical sets with the set of scalar products {α,−α}, α ∈ [0, 1), are called equiangular. The problem of determining the maximal size of s-distance sets in various spaces has a long history in mathematics. We determine a new method of bounding th...
متن کاملPinned distance sets, Wolff’s exponent in finite fields and improved sum-product estimates
An analog of the Falconer distance problem in vector spaces over finite fields asks for the threshold α > 0 such that |∆(E)| & q whenever |E| & q, where E ⊂ Fq , the d-dimensional vector space over a finite field with q elements (not necessarily prime). Here ∆(E) = {(x1 − y1) 2 + · · ·+ (xd − yd) 2 : x, y ∈ E}. The second listed author and Misha Rudnev ([4]) established the threshold d+1 2 , an...
متن کاملPinned distance sets, k-simplices, Wolff’s exponent in finite fields and sum-product estimates
An analog of the Falconer distance problem in vector spaces over finite fields asks for the threshold α > 0 such that |∆(E)| & q whenever |E| & q, where E ⊂ Fq , the d-dimensional vector space over a finite field with q elements (not necessarily prime). Here ∆(E) = {(x1 − y1) 2 + · · · + (xd − yd) 2 : x, y ∈ E}. The fourth listed author and Misha Rudnev ([20]) established the threshold d+1 2 , ...
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: Communications of the Korean Mathematical Society
سال: 2015
ISSN: 1225-1763
DOI: 10.4134/ckms.2015.30.1.023