Paper Info
Title
Trace of products in finite fields.
Abstract
Let p be a prime number and let q=pr. If C and D are large subsets of Fq⁎ we study the trace of products cd with c∈C and d∈D and show that it is well distributed in Fp. We give an optimal condition (up to an absolute constant factor) on the size of the subsets C and D to ensure that the trace of products cd takes any given value in Fp. We also give a condition (optimal up to an absolute constant factor in most cases) on the size of the subsets C and D to ensure that the trace of cd meets the set of k-th powers for k≥1, respectively the set of generators. Our method will enable us to take sets C and D whose size is substantially below q. Character sums and Gaussian sums over Fp and Fq will play an important role in the proofs. Some estimates lead to interesting combinatorial questions in finite fields.
Year
DOI
Venue
2018
10.1016/j.ffa.2018.01.005
Finite Fields and Their Applications
Keywords
Field
DocType
11T30,11T23,11A63
Finite field,Combinatorics,Prime number,Gaussian,Mathematical proof,Trace (linear algebra),Mathematics
Journal
Volume
ISSN
Citations 
51
1071-5797
1
PageRank 
References 
Authors
0.35
0
1
Name
Order
Citations
PageRank
Cathy Swaenepoel110.35