An application of random plane slicing to counting F-q-points on hypersurfaces

作者：Slavov Kaloyan^*

来源：Finite Fields and Their Applications, 2017, 48: 60-67.

DOI：10.1016/j.ffa.2017.07.002

• Hypersurface
• Lang-Weil bound
• Bertini's theorem
• Random sampling

Let X be an absolutely irreducible hypersurface of degree d in A(n), defined over a finite field F-q. The Lang-Weil bound gives an interval that contains #X(F-q). We exhibit an explicit interval, which does not contain #X(F-q), and which overlaps with the Lang-Weil interval. In particular, we sharpen the best known nontrivial lower bound for #X(F-q). The proof uses a combinatorial probabilistic technique.

• 出版日期2017-11