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Inhomogeneous cubic congruences and rational points on del Pezzo surfaces
Inhomogeneous cubic congruences rational points del Pezzo surfaces
2010/11/22
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) and use it to establish the Manin conjecture for a singular d...
A famous result of Hausdorff states that a sphere with countably many points removed can be partitioned into three pieces A,B,C such that A is congruent to B (i.e., there is an isometry of the sphere...
Solutions to congruences using sets with the property of Baire
Solutions sets property of Baire
2010/10/29
Hausdorff's paradoxical decomposition of a sphere with countably many points removed (the main precursor of the Banach-Tarski paradox) actually produced a partition of this set into three pieces A,B,...