ESTIMATES FOR THE NUMBER OF RATIONAL POINTS ON CONVEX CURVES AND SURFACES

摘要

Let Γ is contained in R~d be a bounded strictly convex surface. We prove that the number k_n (Γ) of points of Γ that lie on the lattice 1 Z~2 satisfies the following estimates: liminf k_n(Γ)~(d-2) < ∞ for d ≥ 3 and lim inf k_n(Γ)/log n < ∞ for d = 2. Bibliography: 9 titles.