Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771552 | Finite Fields and Their Applications | 2017 | 19 Pages |
Abstract
We study the k-resultant modulus set problem in the d-dimensional vector space Fqd over the finite field Fq with q elements. Given EâFqd and an integer kâ¥2, the k-resultant modulus set, denoted by Îk(E), is defined asÎk(E)={âx1±x2±â¯Â±xkââFq:xjâE,j=1,2,â¦,k}, where âαâ=α12+â¯+αd2 for α=(α1,â¦,αd)âFqd. In this setting, the k-resultant modulus set problem is to determine the minimal cardinality of EâFqd such that Îk(E)=Fq or Fqâ. This problem is an extension of the ErdÅs-Falconer distance problem. In particular, we investigate the k-resultant modulus set problem with the restriction that the set EâFqd is contained in a specific algebraic variety. Energy estimates play a crucial role in our proof.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
David Covert, Doowon Koh, Youngjin Pi,