On the sum of two primitive elements of maximal subfields of a finite field

  • Authors:

  • B. V. Petrenko

  • Affiliations:

  • Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA

  • Venue:
  • Finite Fields and Their Applications
  • Year:
  • 2003

Quantified Score

Hi-index 0.00

Visualization

Abstract

Let F"r denote a finite field with r elements. Let q be a power of a prime, and p"1,p"2, p"3 be distinct primes. Puty"1=p"1p"2,y"2=p"1p"3,y"3=p"2p"3,y=p"1p"2p"3,A={(t"1,t"2)@?F"q"^"y"^"""^"1xF"q"^"y"^"""^"2|F"q(t"1)=F"q"^"y"^"""^"1,F"q(t"2)=F"q"^"y"^"""^"2,F"q(t"1+t"2)F"q"^"y}.We express the number of elements in A in terms of q, p"1, p"2, p"3 and give several applications to counting points in algebraic sets.