NONSINGULAR ZEROS OF QUINTIC FORMS OVER FINITE FIELDS

DAVID B. LEEP AND CHARLES C. YEOMANS

Abstract:

Let f be a nondegenerate homogeneous polynomial of degree 5 defined over the finite field tex2html_wrap_inline14 in at least six variables. We show that if q>101, then f has a nonsingular tex2html_wrap_inline14 -rational zero.