A Note on the Rational Points

Distribution of Rational Points: A Survey

Points at Rational Distance from the Vertices of a Unit Polygon

1 5 Ju n 20 05 Note on the rational points of a pfaff curve

Let X ⊂ R be the graph of a pfaffian function f in the sense of Khovanskii. Suppose that X is nonalgebraic. This note gives an estimate for the number of rational points on X of height ≤ H ; the estimate is uniform in the order and degree of f . 2000 Mathematics Subject Classification: 11D99 (11J99)

A Note on the Rational Points of X+0(N)

Let C be the image of a canonical embedding φ of the Atkin-Lehner quotient X 0 (N) associated to the Fricke involution wN . In this note we exhibit some relations among the rational points of C. For each g = 3 (resp. the first g = 4) curve C we found that there are one or more lines (resp. planes) in P whose intersection with C consists entirely of rational Heegner points or the cusp point, whe...

Rational Points on Certain Del Pezzo Surfaces of Degree One

Let f(z) = z +az + bz + cz+ d ∈ Z[z] and let us consider a del Pezzo surface of degree one given by the equation Ef : x 2 − y − f(z) = 0. In this note we prove that if the set of rational points on the curve Ea, b : Y 2 = X + 135(2a − 15)X − 1350(5a + 2b − 26) is infinite, then the set of rational points on the surface Ef is dense in the Zariski topology.