Inhomogeneous cubic congruences and rational points on del Pezzo surfaces

Details Inhomogeneous cubic congruences and rational points on del Pezzo surfaces Inhomogeneous cubic congruences and rational points on del Pezzo surfaces

2010-11-15

arxiv.org/abs/1011.3434v2

Mathematics

Number Theory

65 pages

Scientific paper

For given non-zero integers a,b,q we investigate the density of integer
solutions (x,y) to the binary cubic congruence ax^2+by^3=0 (mod q). We use this
to establish the Manin conjecture for a singular del Pezzo surface of degree 2
defined over the rationals and to examine the distribution of elliptic curves
with square-free discriminant.

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